All questions
Question 1
How many sides does a pentagon have?
- 4
- 6
- 5 (correct answer)
- 8
Explanation: A pentagon has 5 sides. Choice A (4) is the number of sides in a square or rectangle. Choice B (6) is the number of sides in a hexagon. Choice D (8) is the number of sides in an octagon.
Question 2
Which object is shaped like a circle?
- window
- coin (correct answer)
- book
- door
Explanation: A coin is round, so it is shaped like a circle. A window, book, and door are usually rectangular, not circular.
Question 3
Ben wants to draw a shape that has exactly 5 angles and 5 sides. He starts by drawing 3 sides. How many more sides does Ben need to draw to finish his shape correctly?
- 2 more sides to complete the pentagon he is making (correct answer)
- 3 more sides to make sure all angles are equal
- 1 more side because he needs to close the shape
- 5 more sides because that's how many the shape needs
Explanation: Ben is making a pentagon, which has 5 sides total. Since he already drew 3 sides, he needs 5 - 3 = 2 more sides. Choice B gives the wrong number and reason. Choice C would only give him 4 sides total. Choice D ignores the sides he already drew.
Question 4
Maya drew a shape with 4 sides. Two of the sides are the same length, and the other two sides are also the same length as each other but different from the first two. All corners are square corners. What shape did Maya draw?
- Square
- Rectangle (correct answer)
- Quadrilateral
- Pentagon
Explanation: Maya's shape has two pairs of equal sides (not all four sides equal) and square corners -- that describes a rectangle. Choice A (square) would require all four sides to be the same length. Choice C (quadrilateral) is true but too general to describe the specific shape. Choice D (pentagon) has 5 sides, not 4.
Question 5
Based on the figure, how many faces does the solid shape have?
- 4 faces
- 6 faces (correct answer)
- 8 faces
- 12 faces
Explanation: When you see a question about a solid shape (a 3D figure), you need to count its faces — the flat surfaces that make up the outside of the shape. A helpful trick is to imagine picking up the shape and turning it in your hands: count the top, the bottom, and each side.
For a cube (or any rectangular box/prism), there are always 6 faces: one on top, one on the bottom, and four around the sides (front, back, left, right). That's why B is correct.
Now let's look at the wrong answers. Choice A (4 faces) is a common mistake when students only count the sides they can see from the front and forget the top and bottom, or confuse faces with something like a pyramid's slanted sides. Choice C (8 faces) confuses faces with vertices (corners) — a cube has 8 corners, but corners aren't faces. Choice D (12 faces) confuses faces with edges — a cube has 12 edges (the lines where two faces meet), but edges aren't faces either.
A great memory tool for cubes and rectangular prisms is "6-8-12": 6 faces, 8 vertices (corners), 12 edges. If a question asks about any of these three parts, you can quickly match the number to the correct part. Always read carefully to see whether the question wants faces, corners, or edges — that's the most common trap on solid-shape questions.
Question 6
The figure shows four shapes. How many of the shapes are triangles?
- 1 shape
- 4 shapes
- 3 shapes
- 2 shapes (correct answer)
Explanation: When you're asked to identify triangles, remember the rule: a triangle is a closed shape with exactly 3 straight sides and 3 corners (vertices). Shapes with curves, four sides, or open lines don't count — even if they look pointy or similar to a triangle.
To solve this kind of problem, check each shape one at a time and ask: "Does it have 3 straight sides that connect to form a closed figure?" Count only the ones that pass this test. In this figure, two of the four shapes meet all the triangle rules, which is why D (2 shapes) is correct.
Now let's look at the traps:
- A (1 shape) is wrong because you likely only counted the "typical" upward-pointing triangle and missed a second triangle that was tilted, flipped, or a different size. Triangles come in many orientations!
- B (4 shapes) is wrong because it assumes every shape in the picture is a triangle. Some shapes have 4 sides or curves, so they don't qualify.
- C (3 shapes) is wrong because it counts a shape that only looks triangle-like — maybe one with a curved side or an open side — as a real triangle.
Study tip: When counting shapes, don't trust your eyes alone — count the sides and corners of each figure. A shape is only a triangle if you can count exactly 3 straight sides and 3 corners, no matter which way it's turned. Question 7
Tommy is building with blocks. He wants to use only blocks that are cubes. He finds 4 blocks: one shaped like a ball, one shaped like a can, one shaped like a box with square faces, and one shaped like a pyramid. Which block should Tommy choose?
- The ball-shaped block
- The can-shaped block
- The box with square faces (correct answer)
- The pyramid-shaped block
Explanation: A cube has flat, square faces on every side, and the box with square faces is the only block built that way. A ball is round and has no flat faces at all. A can has flat circular ends but curved sides, so it isn't a cube. A pyramid has flat faces too, but they are triangles that meet at a point, not a cube's square faces.
Question 8
Look at the shape below. How many sides and angles does it have, and what is its name?
- 6 sides, 6 angles — hexagon (correct answer)
- 5 sides, 5 angles — pentagon
- 6 sides, 5 angles — pentagon
- 4 sides, 4 angles — quadrilateral
Explanation: A hexagon has 6 sides and 6 angles. The number of sides and angles in a polygon is always the same.
Question 9
The diagram shows a group of shapes inside a circle labeled "Quadrilaterals." One shape does NOT belong in the group. Which shape should be removed?
- The square
- The rectangle
- The pentagon (correct answer)
- The trapezoid
Explanation: When you see a group of shapes labeled with a category name, your job is to check each shape against the definition of that category. A quadrilateral is any closed shape with exactly 4 straight sides and 4 corners (vertices). If a shape has more or fewer sides, it doesn't belong in the quadrilateral group.
Go through each shape and count its sides. A pentagon has 5 sides and 5 corners, so it breaks the "4-sides" rule. That means the pentagon is the shape that doesn't fit and should be removed, making C the correct choice.
Now look at why the others do belong:
- A (square) has 4 equal sides and 4 corners, so it's a quadrilateral. It belongs in the circle.
- B (rectangle) also has 4 sides and 4 corners — the sides just aren't all equal. Still a quadrilateral.
- D (trapezoid) has exactly 4 sides too (with one pair of parallel sides). It's a quadrilateral, so it stays.
A helpful memory trick: the prefix "quad-" means four (like a quad bike with 4 wheels), and "penta-" means five (like the Pentagon building with 5 sides). So a pentagon can never be a quadrilateral.
Study tip: Whenever a shape question uses a group name, translate the name into a rule about number of sides first. Count the sides of every shape, and the odd one out will jump right off the page. Question 10
Refer to the figure. Which shape has MORE angles than a quadrilateral but FEWER angles than a hexagon?
- Shape A
- Shape B (correct answer)
- Shape C
- Shape D
Explanation: When a question asks about angles in shapes, remember that the number of angles in a shape equals the number of sides (and corners). A quadrilateral has 4 angles, and a hexagon has 6 angles. So you're looking for a shape with exactly 5 angles — a pentagon.
Since Shape B is the pentagon in the figure, it fits perfectly: 5 is more than 4 (quadrilateral) but fewer than 6 (hexagon).
Shape A is a quadrilateral (4 angles), so it has the same number of angles as a quadrilateral, not more. Shape C is a hexagon (6 angles), which matches a hexagon rather than having fewer. Shape D is likely a triangle or another shape with 3 angles, which is fewer than a quadrilateral, so it doesn't meet the "more than a quadrilateral" part of the rule.
A helpful memory tip: the prefix tells you the number of angles! Tri- = 3, Quad- = 4, Penta- = 5, Hexa- = 6. When a question uses "between" or "more than… but fewer than…," pick the number in the middle and match it to the shape name.
Question 11
In the diagram, each face of the solid is a square, and all faces are the same size. What is the name of this solid?
- Cube (correct answer)
- Hexagon
- Pentagon
- Rectangle
Explanation: When you see a question about naming a solid (a 3D shape), pay close attention to two clues: the shape of the faces and how many faces there are. Solids are named based on their overall 3D structure, not just one face.
Here, every face is a square and all faces are the same size. A solid with 6 identical square faces is called a cube. Think of dice, sugar cubes, or a Rubik's cube — all perfect examples. That makes A the correct choice.
Now look at why the others don't fit. B (Hexagon) is a flat 2D shape with 6 straight sides, not a solid — you can't build a 3D object just by saying "hexagon." C (Pentagon) is also a flat 2D shape, with 5 sides. Both hexagons and pentagons are polygons, meaning they live on paper, not in space. D (Rectangle) is another 2D shape — a flat figure with four sides where opposite sides are equal. A rectangle isn't a solid at all, and even the 3D version (a rectangular prism) wouldn't have all square faces of the same size.
A helpful tip: remember that 2D shapes are flat (hexagon, pentagon, rectangle, square) and 3D solids take up space (cube, sphere, cylinder, cone). If a question describes faces, edges, or something you could hold in your hand, you're looking for a solid — never a flat shape.
Question 12
A quadrilateral is a shape with 4 straight sides. Sarah drew a shape with only 3 sides. How many more sides does she need to add to make it a quadrilateral?
- 1 more side (correct answer)
- 2 more sides
- 3 more sides
- It cannot become a quadrilateral
Explanation: A quadrilateral needs exactly 4 sides, and Sarah's shape has 3, so she needs 1 more side. Choice B, 2 more sides, would give her too many sides. Choice C, 3 more sides, would also give her too many sides. Choice D is wrong because a shape can be redrawn to have any number of sides.
Question 13
How many corners does a square have?
- 4 (correct answer)
- 3
- 2
- 5
Explanation: A square has 4 corners, one at each point where two sides meet. 3 corners would make a triangle, not a square. 2 corners is not enough for any closed shape. 5 corners belongs to a pentagon, not a square.
Question 14
Refer to the figure. Which statement about the shape is TRUE?
- It is a pentagon because it has 5 sides.
- It is a quadrilateral because it has 4 sides. (correct answer)
- It is a hexagon because it has 6 sides.
- It is a triangle because it has 3 sides.
Explanation: When you see a question asking you to identify a shape, the key is to count its sides carefully and match that number to the shape's name. Each polygon has a specific number of sides:
- Triangle = 3 sides
- Quadrilateral = 4 sides
- Pentagon = 5 sides
- Hexagon = 6 sides
Since the figure has 4 sides, it belongs to the quadrilateral family (which includes squares, rectangles, rhombuses, and trapezoids — any closed shape with exactly four straight sides). That makes B the true statement.
Now let's look at why the others don't work. A is wrong because a pentagon must have 5 sides, but this shape only has 4. C is wrong because a hexagon needs 6 sides — that's two more than this shape has. D is wrong because a triangle has only 3 sides, one fewer than this figure.
A helpful memory trick: the beginning of each shape's name often hints at the number of sides. "Tri-" means 3 (like a tricycle with 3 wheels), "quad-" means 4 (like a quad bike with 4 wheels), "penta-" means 5, and "hexa-" means 6. Whenever you see a shape question, slow down and count each side by touching or marking it — miscounting is the most common mistake on geometry questions like this. Question 15
Refer to the figure showing four shapes labeled 1, 2, 3, and 4. Which shape is a quadrilateral but is NOT a rectangle?
- Shape 1
- Shape 2
- Shape 3 (correct answer)
- Shape 4
Explanation: When you see a shape question like this, remember two key definitions. A quadrilateral is any closed shape with exactly 4 straight sides. A rectangle is a special quadrilateral where all 4 corners are square (right angles) and opposite sides are equal. So every rectangle is a quadrilateral, but not every quadrilateral is a rectangle — shapes like trapezoids, rhombuses, and parallelograms also have 4 sides but lack the right angles.
To answer this question, you need to find a shape that has 4 sides (making it a quadrilateral) but does NOT have four square corners (so it's not a rectangle). Shape 3 fits this description — it has 4 sides but its angles aren't all right angles, so it's a quadrilateral that isn't a rectangle, making C correct.
Here's why the others don't work: A (Shape 1) is a rectangle itself — it has 4 sides AND 4 right angles, so it fails the "NOT a rectangle" part. B (Shape 2) is also a rectangle (a square counts as a rectangle since it has 4 right angles), so it doesn't qualify. D (Shape 4) isn't a quadrilateral at all — it has a different number of sides (like a triangle or pentagon), so it fails the first requirement.
Tip: When a question asks for a shape that "is X but NOT Y," check both conditions separately. Count the sides first to check the general category, then check angles or side lengths for the special category.
Question 16
Use the figure to answer the question. Together, how many total sides do the three shapes have?
- 12 sides
- 15 sides
- 14 sides
- 13 sides (correct answer)
Explanation: When a question asks about the total number of sides across several shapes, you're really being asked to identify each shape, count its sides, and then add those counts together. This tests both your shape recognition and your addition skills.
Since the figure shows three shapes that add up to 13 sides, the combination must be something like a triangle (3 sides), a square or rectangle (4 sides), and a hexagon (6 sides): 3+4+6=13. Another possible combo is a triangle, pentagon, and pentagon: 3+5+5=13. Either way, the sides total 13, which matches D.
Choice A (12) would happen if you miscounted one shape as having one fewer side — for example, counting a hexagon as a pentagon. Choice B (15) is too high; you'd get this by overcounting, like treating a shape as an octagon when it isn't. Choice C (14) is a common near-miss answer, off by just one side, usually from counting an edge twice or mistaking a pentagon for a hexagon.
A helpful strategy: when counting sides on a shape, put a small tick mark or dot on each side as you count so you don't count the same side twice or skip one. Then write each shape's number down before adding — this prevents you from losing track. Memorizing side counts for common shapes (triangle = 3, quadrilateral = 4, pentagon = 5, hexagon = 6) makes these questions much faster. Question 17
Look at the shape in the figure. How many angles does this shape have, and what is its name?
- 5 angles; pentagon (correct answer)
- 6 angles; hexagon
- 5 angles; hexagon
- 6 angles; pentagon
Explanation: When you're asked to identify a shape, there are two things to check: how many sides it has and how many angles ("corners") it has. For most simple closed shapes, the number of sides equals the number of angles. Then you match that number to the shape's name:
- 3 sides/angles → triangle
- 4 sides/angles → quadrilateral
- 5 sides/angles → pentagon
- 6 sides/angles → hexagon
Counting the corners of the figure carefully, you'll find 5 angles, and a 5-angled shape is called a pentagon. That makes A correct.
Now let's look at the traps:
- B (6 angles; hexagon) miscounts the corners as 6. A hexagon has one more side/angle than what's shown.
- C (5 angles; hexagon) counts correctly but uses the wrong name — 5 angles is not a hexagon.
- D (6 angles; pentagon) mixes things up the other way — "pentagon" is the right family of name, but pentagons don't have 6 angles.
Study tip: Remember shape names by their prefixes: penta- means 5 (like the Pentagon building, which has 5 sides), and hexa- means 6. When you see a shape question, always count the corners by touching each one once so you don't count any twice — then match the number to the correct name. Question 18
Refer to the figure. Which shape has the SAME number of angles as the shape shown?
- A hexagon
- A square
- A pentagon (correct answer)
- A triangle
Explanation: When a question asks you to match shapes by their number of angles, remember that in flat (2D) shapes, the number of angles always equals the number of sides. So counting corners is the same as counting sides!
Since the figure shown is a pentagon (a 5-sided shape with 5 angles), you need to find another shape with exactly 5 angles. A pentagon has 5 angles, making C the correct match. Think of it this way: "penta" means five, just like a pentagon in sports (like the Pentagon building) has five sides.
Now let's check the others. A) A hexagon has 6 angles ("hex" means six), which is one too many. B) A square has 4 angles — all right angles — so it falls short by one. D) A triangle has only 3 angles ("tri" means three), the fewest of any polygon, so it doesn't match either.
A helpful study tip: memorize the shape prefixes because they tell you the number of sides and angles every time. Tri = 3 (triangle), quad = 4 (quadrilateral/square), penta = 5 (pentagon), hexa = 6 (hexagon), octa = 8 (octagon). When you see a shape question, count the corners carefully and match the prefix to the number!
Question 19
Mr. Garcia asks his students to sort shapes into two groups: shapes with 3 sides (triangles) and shapes with 4 sides (quadrilaterals). He shows a shape with 3 straight sides and 3 angles. Which of these shapes belongs in the same group as that shape?
- A shape with 3 straight sides and 3 angles (correct answer)
- A shape with 4 straight sides, all the same length
- A shape with 4 sides and 4 right angles
- A shape with 6 straight sides
Explanation: A shape with 3 straight sides and 3 angles matches the triangle group, since it has the same defining features. A shape with 4 equal sides belongs in the 4-sided group instead, not with triangles. A shape with 4 sides and 4 right angles is a rectangle, which also belongs in the 4-sided group. A shape with 6 sides has even more sides than either group described here.
Question 20
A shape has 6 sides and 6 angles. What is the correct name for this shape?
- Pentagon
- Hexagon (correct answer)
- Quadrilateral
- Triangle
Explanation: A hexagon is a shape with exactly 6 sides and 6 angles. Choice A, pentagon, has 5 sides, not 6. Choice C, quadrilateral, has 4 sides, not 6. Choice D, triangle, has only 3 sides.