Geometry Riddles

Ten geometry riddles at a time: shapes, solids, angles and circles, each answer hidden until you tap it.

Geometry Riddles

Show all 98
  1. Two angles of a triangle measure 90 degrees and 45 degrees. How big is the third angle?
  2. How many sides do a triangle, a square and a pentagon have altogether?
  3. I have four sides, and two of them run side by side like train tracks while the other two lean in. I look like a triangle with its top sliced off. What shape am I?
  4. Join each of my five corners to the corners that are not next to it, and a five-pointed star appears inside me. What shape am I?
  5. I am one flat side of a solid shape. A cube has six of me, and a pyramid on a square has five. What am I?
  6. I am half of a circle, with one straight side and one curved side. A protractor has my shape. What shape am I?
  7. I have five faces, five corners and eight edges. One of my faces is a square and the other four are triangles. What solid shape am I?
  8. Any four-sided shape can be cut into two triangles by one straight line from corner to corner. What do its four angles add up to?
  9. I am any flat, closed shape made only of straight sides. I can have three sides or a hundred, and a circle can never join my club. What am I?
  10. A tic-tac-toe board with a frame around it has nine small squares. Counting squares of every size, how many squares are in the picture?

Next step Number riddlesMath trivia with four choices

How it works

These geometry riddles start with what shape am I and go on to the rest of a geometry unit. Under each answer, one line gives the definition or the count that settles it.

Read the full guide

Shape riddles first, then the rest of geometry

Flat shapes and Solid shapes are the shape riddles: each names a shape by its sides, its corners or a thing at home that has it. Lines, angles and measures and Parts of a circle ask for the words of the unit: perpendicular, vertex, radius, chord.

Count and think

The last set has puzzles with a number for an answer: squares on a tic-tac-toe board, posts around a pen, the angles of a hexagon.

  • Draw it. Most of these fall to a quick sketch, and the counting puzzles nearly always do.

Questions and answers

What is a good geometry riddle?

One with a single sure answer. I am a rectangle and a rhombus at the same time. What shape am I? A square: only a square has four right angles and four equal sides.

What is a rectangular riddle?

A riddle answered by a rectangle or a box shape. I am the shape of a door, a dollar bill and a playing card. What shape am I? Four riddles here are answered by a rectangle and one by a rectangular prism.

What is an easy shape riddle for kids?

I have six sides and six corners, and bees build their wax rooms in my shape. What shape am I? A hexagon. The Easy level names shapes by things a child knows: a coin, a party hat, a soup can.

What is a hard geometry riddle?

What is the most pieces you can get from a pizza with three straight cuts, if the pieces do not have to be the same size? Seven: every cut has to cross the ones before it, and not at the same spot.

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All 98 riddles

Flat shapes 38

  • Add up my three angles and you get 180 degrees every time, however long or short you draw my sides. What shape am I? Answer: A triangle. The angles inside any flat triangle add up to 180 degrees.
  • All four of my sides are the same length, but my corners do not have to be square. Many people call me a diamond. What shape am I? Answer: A rhombus. A rhombus has four equal sides; diamond is its everyday name.
  • All three of my sides are the same length, and each of my angles is 60 degrees. What kind of triangle am I? Answer: An equilateral triangle. Equilateral means equal sides, and three equal angles share 180 degrees as 60 each.
  • Cut me from corner to corner and you get two right triangles that match exactly. All four of my corners are right angles. What shape am I? Answer: A rectangle. A diagonal splits a rectangle into two equal right triangles.
  • Cut the four corners off a square, all by the right amount, and I am what is left, with eight equal sides. What shape am I? Answer: An octagon. Four old sides plus four new cut sides make eight.
  • Fit six triangles with equal sides around one point, like slices of a pie, and together they make me. What shape am I? Answer: A hexagon. A regular hexagon can be cut into six equilateral triangles.
  • I am a rectangle and a rhombus at the same time. What shape am I? Answer: A square. A rectangle has four right angles and a rhombus has four equal sides; only a square has both.
  • I am any flat, closed shape made only of straight sides. I can have three sides or a hundred, and a circle can never join my club. What am I? Answer: A polygon. A polygon is closed and has only straight sides, so a curve is not allowed.
  • I am half of a circle, with one straight side and one curved side. A protractor has my shape. What shape am I? Answer: A semicircle. Semi means half.
  • I am the red shape on a playing card that is not a heart. In math class I go by another name. What shape am I? Answer: A diamond, which is a rhombus. The diamond on a card has four equal slanted sides.
  • I am the shape of a clock face, a coin and the lid of a jar. What shape am I? Answer: A circle. All three are round and flat, with no corners.
  • I am the shape of a door, a dollar bill and a playing card. What shape am I? Answer: A rectangle. Each has four square corners and is longer one way than the other.
  • I am the shape of a popcorn bucket seen from the side: wide at the top, narrow at the bottom, flat on both. What shape am I? Answer: A trapezoid. The top and the bottom are parallel, and the two sides slant.
  • I am the shape of a tortilla chip, a clothes hanger and a sandwich cut from corner to corner. What shape am I? Answer: A triangle. Each has three sides and three corners.
  • I am the shape of one space on a checkerboard, a sticky note and a slice of sandwich cheese. What shape am I? Answer: A square. Each is as wide as it is tall, with four square corners.
  • I am the shape of the moon when only a thin curved sliver shows. What shape am I? Answer: A crescent. A crescent is a curved shape that is thick in the middle and comes to two points.
  • I have eight sides and eight corners. A red sign in my shape tells drivers to stop. What shape am I? Answer: An octagon. Octa means eight, and a stop sign is a red octagon.
  • I have five sides and five corners. Draw a square house with a pointed roof in one outline, and you have drawn me. What shape am I? Answer: A pentagon. Count the outline of the house: two walls, a floor and two roof lines make five sides.
  • I have four sides and four corners like the corner of a page. My opposite sides match, and I am usually longer than I am wide. What shape am I? Answer: A rectangle. A rectangle has four right angles and two pairs of equal sides.
  • I have four sides that are all the same length and four corners like the corner of a page. What shape am I? Answer: A square. Four equal sides and four right angles make a square.
  • I have four sides, and two of them run side by side like train tracks while the other two lean in. I look like a triangle with its top sliced off. What shape am I? Answer: A trapezoid. A trapezoid has a pair of parallel sides. In British English it is a trapezium.
  • I have no corners and no straight sides. Every point on my edge is the same distance from my middle. What shape am I? Answer: A circle. A circle is every point at one fixed distance from its center.
  • I have seven sides and seven corners, and some people call me a septagon. What shape am I? Answer: A heptagon. Hepta is Greek for seven.
  • I have six sides and six corners, and bees build their wax rooms in my shape. What shape am I? Answer: A hexagon. The cells of a honeycomb are hexagons.
  • I have ten sides and ten corners, and my name starts like the word decade. What shape am I? Answer: A decagon. Deca means ten: a decade is ten years, a decagon has ten sides.
  • I have three sides and three corners, and my name starts with the word part for three. What shape am I? Answer: A triangle. Tri means three: three sides, three angles.
  • I look like a circle that somebody stretched. A serving platter and a bathroom mirror often have my shape. What shape am I? Answer: An oval. An oval is round with no corners, and longer one way than the other.
  • Join each of my five corners to the corners that are not next to it, and a five-pointed star appears inside me. What shape am I? Answer: A pentagon. The five diagonals of a regular pentagon draw a star called a pentagram.
  • My opposite sides are equal and parallel, and my opposite angles match. The rectangle, the rhombus and the square all belong to my family. What shape am I? Answer: A parallelogram. Each of those three is a parallelogram with something extra.
  • My two diagonals are the same length and cut each other in half, yet my four sides do not have to be equal. What shape am I? Answer: A rectangle. Equal diagonals that bisect each other are the mark of a rectangle.
  • No two of my sides are the same length, and no two of my angles match. What kind of triangle am I? Answer: A scalene triangle. Scalene is the name for a triangle with three different sides.
  • One of my corners is square, like the corner of a book. My longest side sits across from that corner and is called the hypotenuse. What kind of triangle am I? Answer: A right triangle. A right triangle has one 90-degree angle, and the side facing it is the hypotenuse.
  • Push a rectangle sideways so that it leans, and you have me. My opposite sides still run side by side and never meet. What shape am I? Answer: A parallelogram. A parallelogram has two pairs of parallel sides.
  • Push two tacks into a board, drop a loop of string over them and pull it tight with a pencil. Move the pencil all the way around. What shape does it draw? Answer: An ellipse. This is the gardener's way to draw an ellipse: the two tacks mark its two focus points.
  • Squares, rectangles, kites and trapezoids all belong to my family, because each one has four sides. What is our family name? Answer: Quadrilateral. A quadrilateral is any shape with four straight sides.
  • Tie a pencil to a string, pin the other end of the string to the paper and keep the string tight. What shape does the pencil draw? Answer: A circle. The string keeps the pencil the same distance from the pin all the way around.
  • Two of my sides are twins, and the third is the odd one out. What kind of triangle am I? Answer: An isosceles triangle. An isosceles triangle has two sides of equal length.
  • Two short sides meet at my top and two long sides meet at my bottom. I am named after a toy that flies on a string. What shape am I? Answer: A kite. A kite has two pairs of equal sides, and the equal sides are next to each other.

Solid shapes 18

  • Cut a ball exactly in half and you get two of me. A bowl turned upside down has my shape. What solid shape am I? Answer: A hemisphere. Hemi means half, so a hemisphere is half a sphere.
  • I am one flat side of a solid shape. A cube has six of me, and a pyramid on a square has five. What am I? Answer: A face. The flat surfaces of a solid are its faces.
  • I am round all over like a ball. I have no flat face, no edge and no corner. What solid shape am I? Answer: A sphere. A sphere is perfectly round in every direction.
  • I am the line where two faces of a solid shape meet. A cube has twelve of me. What am I? Answer: An edge. Run a finger along the fold of a box: that line is an edge.
  • I am the shape of a doughnut and an inner tube: round all the way around, with a hole through my middle. What solid shape am I? Answer: A torus. Torus is the math name for a ring shape like a doughnut.
  • I am the shape of a marble, an orange and a globe. What solid shape am I? Answer: A sphere. Each one is round like a ball.
  • I am the shape of a shoebox, a brick and a cereal box. I have six faces, and each one is a rectangle. What solid shape am I? Answer: A rectangular prism. A box shape with six rectangular faces is a rectangular prism, also called a cuboid.
  • I am the shape of a sugar lump, a number die and a toy building block with square sides. What solid shape am I? Answer: A cube. Each one has six square faces.
  • I have 6 faces, 12 edges and 8 corners, and all my edges are the same length. What solid shape am I? Answer: A cube. Count them on a box with square sides: 6 faces, 12 edges, 8 corners.
  • I have a square to stand on and four triangle faces that lean in to meet at one point. What solid shape am I? Answer: A pyramid. This is a square pyramid, the shape of the great stone tombs of Egypt.
  • I have five faces, five corners and eight edges. One of my faces is a square and the other four are triangles. What solid shape am I? Answer: A square pyramid. Four corners on the base and one at the top; four edges around the base and four that climb.
  • I have one flat circle to stand on and one point at the top. A party hat has my shape. What solid shape am I? Answer: A cone. A cone narrows from a round base to a single point.
  • I have only four faces, and every one of them is a triangle. No solid with flat faces can have fewer. What solid shape am I? Answer: A tetrahedron. A tetrahedron is a pyramid on a triangle base: 4 faces, 6 edges, 4 corners.
  • I have six faces, and every one of them is a square of the same size. What solid shape am I? Answer: A cube. A cube is made of six equal squares.
  • I have two flat ends that are circles and one curved side between them. A soup can has my shape. What solid shape am I? Answer: A cylinder. A can is a cylinder: two round ends joined by a curved wall.
  • Roll a rectangle of paper into a tube and tape its edges, and you have made my side. Two circles close my ends. What solid shape am I? Answer: A cylinder. Unrolled, the curved side of a cylinder is a rectangle.
  • Slice me straight through anywhere you like, and the cut face is always a circle. What solid shape am I? Answer: A sphere. Every flat slice of a sphere is a circle.
  • Two of my faces are triangles and three are rectangles. A wedge of cheese and an old-style ridge tent have my shape. What solid shape am I? Answer: A triangular prism. A triangular prism has a triangle at each end and three rectangles between them.

Lines, angles and measures 16

  • A full turn has 360 of me, a right angle has 90, and my sign is a tiny raised circle. What am I? Answer: A degree. Angles are measured in degrees, written with the sign °.
  • A line goes on forever in both directions, but I do not. I have two endpoints, and you can measure me with a ruler. What am I? Answer: A line segment. A line segment is the part of a line between two points.
  • Fold a paper heart along me and the two halves match exactly. A square has four of me. What am I? Answer: A line of symmetry. A line of symmetry splits a shape into two mirror halves, and a square can be folded to match in four ways.
  • I am a half circle of clear plastic with degrees marked along my curved edge. You use me to measure angles. What am I? Answer: A protractor. A protractor measures angles in degrees.
  • I am a straight line drawn inside a shape from one corner to a corner that is not next door. A square has two of me, and a triangle has none. What am I? Answer: A diagonal. A diagonal joins two corners that do not share a side.
  • I am an angle narrower than the corner of a page: less than 90 degrees. The hands of a clock make me at one o'clock. What angle am I? Answer: An acute angle. An angle smaller than a right angle is acute.
  • I am an angle that looks like a straight line. I measure exactly 180 degrees, the same as two right angles side by side. What angle am I? Answer: A straight angle. Half of a full turn is a straight angle.
  • I am the amount of flat space inside a shape. For a rectangle, multiply the length by the width to find me. What am I? Answer: The area. Area is measured in squares: a 3 by 4 rectangle covers 12 of them.
  • I am the angle at the corner of a page, a door and a square: exactly 90 degrees. What angle am I? Answer: A right angle. A right angle is a quarter of a full turn.
  • I am the distance all the way around a shape. To find me, add up the lengths of the sides. What am I? Answer: The perimeter. Perimeter is the length of the outline of a shape.
  • I am the point where two sides of a shape meet, or the two arms of an angle. A triangle has three of me, and my plural is vertices. What am I? Answer: A vertex. Vertex is the math word for a corner.
  • I am wider than a right angle and not yet a straight line: more than 90 degrees and less than 180. What angle am I? Answer: An obtuse angle. Obtuse angles open wider than a right angle.
  • I have a place and no size at all: no length, no width, no height. You mark me with a dot and name me with a capital letter. What am I? Answer: A point. A point shows a position and has no size.
  • I start at one point and go on forever in one direction only. What am I? Answer: A ray. A ray has a starting point and no end, like a beam of light.
  • We are two lines that cross and make four square corners, like the two strokes of a plus sign. What are we? Answer: Perpendicular lines. Perpendicular lines meet at right angles.
  • We are two lines that run side by side forever, always the same distance apart, and never meet. Train tracks look like us. What are we? Answer: Parallel lines. Parallel lines never cross, however far they go.

Parts of a circle 12

  • Divide the distance around any circle by the distance across it and you get me every time: a little more than 3. I am named with a Greek letter. What number am I? Answer: Pi. Pi is the circumference divided by the diameter, about 3.14.
  • I am a piece of the edge of a circle: the curve between two points on it. What am I? Answer: An arc. An arc is part of the circumference.
  • I am a slice of a circle shaped like a piece of pie, with two straight sides that meet at the center and a curved crust. What am I? Answer: A sector. A sector is the part of a circle between two radii and an arc.
  • I am a straight line from the center of a circle to its edge. Two of me, end to end, reach all the way across. What am I? Answer: A radius. The radius is half the diameter.
  • I am a straight line that joins two points on a circle. I do not have to pass through the center, and the diameter is the longest of my kind. What am I? Answer: A chord. Any straight line between two points on a circle is a chord.
  • I am a straight line that touches a circle at exactly one point and never goes inside it. What am I? Answer: A tangent. A tangent just touches the circle and runs on.
  • I am the distance all the way around a circle. Wrap a string once around a can to measure me. What am I? Answer: The circumference. Circumference is the perimeter of a circle.
  • I am the one point inside a circle that is the same distance from every point on its edge. What am I? Answer: The center. Every radius starts at the center.
  • I cross a circle from edge to edge through its center, and I am the longest straight line that fits inside it. What am I? Answer: A diameter. A diameter passes through the center and is the longest chord of the circle.
  • I have two legs, one with a sharp point and one that holds a pencil. Swing me around and I draw a circle. What am I? Answer: A drawing compass. The point stays on the center while the pencil draws the edge.
  • Two diameters cross at right angles and cut a circle into four equal parts. I am one of the four. What am I? Answer: A quadrant. A quadrant is a quarter of a circle.
  • We are circles of different sizes that share one center, like the rings of an archery target. What are we? Answer: Concentric circles. Concentric means having the same center.

Count and think 14

  • A circle with a radius of 5 inches fits exactly inside a square and touches all four sides. What is the perimeter of the square? Answer: 40 inches. The side of the square is as long as the diameter of the circle, 2 × 5 = 10 inches, and 4 × 10 = 40.
  • A farmer builds a square pen with 4 fence posts along each side. How many posts does the pen need? Answer: 12. Each corner post is shared by two sides, so it is 4 corners plus 2 more on each side: 4 + 8 = 12, not 16.
  • A hexagon can be cut into four triangles, so its six angles add up to 4 × 180 degrees. If all six angles are equal, how big is each one? Answer: 120 degrees. 4 × 180 = 720, and 720 ÷ 6 = 120.
  • A square can be folded in half four ways so that the two halves match. In how many ways can a rectangle that is not a square? Answer: 2. Fold it across the middle either way. A fold from corner to corner does not work: the halves do not land on each other.
  • A square has a perimeter of 20 inches. What is its area? Answer: 25 square inches. Each side is 20 ÷ 4 = 5 inches, and 5 × 5 = 25.
  • A tic-tac-toe board with a frame around it has nine small squares. Counting squares of every size, how many squares are in the picture? Answer: 14. Nine small squares, four squares that are 2 by 2 and the one big square: 9 + 4 + 1 = 14.
  • Any four-sided shape can be cut into two triangles by one straight line from corner to corner. What do its four angles add up to? Answer: 360 degrees. Each triangle has 180 degrees, and 2 × 180 = 360.
  • Draw three straight lines across a page. What is the most places they can cross each other? Answer: 3. Each pair of lines can cross once, and three lines make three pairs.
  • Four small squares of the same size are pushed together to make one big square. The big square has a perimeter of 16 inches. What is the perimeter of one small square? Answer: 8 inches. The big square is 4 inches on a side, so each small square is 2 inches on a side, and 2 + 2 + 2 + 2 = 8.
  • From one corner of a hexagon, draw a straight line to every corner that is not next to it. Into how many triangles is the hexagon cut? Answer: 4. Three lines can be drawn, and they cut the hexagon into 4 triangles: always two fewer than the number of sides.
  • How many diagonals can you draw inside a pentagon? Answer: 5. Each of the 5 corners has 2 corners that are not next to it, and every diagonal is counted from both ends: 5 × 2 ÷ 2 = 5.
  • How many sides do a triangle, a square and a pentagon have altogether? Answer: 12. 3 + 4 + 5 = 12.
  • Two angles of a triangle measure 90 degrees and 45 degrees. How big is the third angle? Answer: 45 degrees. The three angles add up to 180, and 180 − 90 − 45 = 45.
  • What is the most pieces you can get from a pizza with three straight cuts, if the pieces do not have to be the same size? Answer: 7. Make every cut cross the ones before it, and not at the same spot: 2 pieces, then 4, then 7.