Geometry – Understanding Shapes Quiz - ICSE Class 8 Mathematics

Free practice quiz: Geometry – Understanding Shapes (ICSE Class 8 Mathematics). 49 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 8 Mathematics practice quiz has 49 multiple-choice questions on Geometry – Understanding Shapes, and 49 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. The perimeter of a square is 48 cm. What is its area?

   1. 144 cm²
   2. 12 cm²
   3. 576 cm²
   4. 24 cm²
   Show answer

   Answer: A. 144 cm²

   Perimeter of a square = 4 * side. So, 4 * side = 48 cm. Side = 48 cm / 4 = 12 cm. Area of a square = side * side = 12 cm * 12 cm = 144 cm².

2. A square has a diagonal of length 10√2 cm. What is its area?

   1. 50 cm²
   2. 100 cm²
   3. 200 cm²
   4. 25√2 cm²
   Show answer

   Answer: B. 100 cm²

   In a square, if the side is 's', the diagonal is s√2. So, s√2 = 10√2 cm. This means s = 10 cm. The area of the square is s² = (10 cm)² = 100 cm².

3. Which of the following statements is true for a trapezoid?

   1. Exactly one pair of opposite sides are parallel.
   2. Both pairs of opposite sides are parallel.
   3. All sides are equal in length.
   4. All angles are equal.
   Show answer

   Answer: A. Exactly one pair of opposite sides are parallel.

   A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. A parallelogram has both pairs parallel.

4. A regular pentagon has an interior angle of 108°. What is the measure of each exterior angle?

   1. 72°
   2. 108°
   3. 180°
   4. 60°
   Show answer

   Answer: A. 72°

   An interior angle and its corresponding exterior angle form a linear pair (add up to 180°). So, Exterior angle = 180° - Interior angle = 180° - 108° = 72°.

5. What is the net of a cube?

   1. A single square.
   2. A rectangle divided into 6 equal squares.
   3. A shape formed by 6 squares joined edge-to-edge.
   4. A circle divided into sectors.
   Show answer

   Answer: C. A shape formed by 6 squares joined edge-to-edge.

   A net of a 3D shape is a 2D pattern that can be folded to form the shape. The net of a cube consists of 6 squares arranged in a way that they can be folded into a cube.

More questions in this quiz

Answers and explanations are in the full quiz.

1. A triangle has angles measuring 55°, 65°, and x°. What is the value of x?
2. Which of the following is NOT a property of a rhombus?
3. The area of a parallelogram is 72 cm². If its base is 9 cm, what is its height?
4. A circle has a radius of 7 cm. If pi (π) is taken as 22/7, what is its circumference?
5. How many edges does a cuboid have?
6. If the sum of the interior angles of a regular polygon is 1080°, how many sides does it have?
7. What is the angle of each interior angle of a regular hexagon?
8. Two angles of a triangle are 30° and 70°. What is the measure of the third angle?
9. Which 3D shape has only one vertex?
10. A kite has diagonals of length 10 cm and 12 cm. What is its area?
11. The sum of the interior angles of a pentagon is 540°. What is the measure of each interior angle of a regular pentagon?
12. If a triangle has sides of length 5 cm, 12 cm, and 13 cm, what type of triangle is it?
13. What is the sum of the exterior angles of any convex polygon?
14. A circle has a diameter of 14 cm. What is its area? (Use π = 22/7)
15. Which of the following is an example of a regular polygon?
16. If the area of a rhombus is 84 cm² and one of its diagonals is 12 cm, what is the length of the other diagonal?
17. A rectangle has a perimeter of 30 cm. If its length is 9 cm, what is its area?
18. A cube has a volume of 216 cm³. What is the length of one of its edges?
19. The angle at the center of a circle subtended by an arc is 90°. What is the angle subtended by the same arc at any point on the remaining part of the circle?
20. What is the measure of each exterior angle of a regular octagon?
21. A sector of a circle has a radius of 10 cm and a central angle of 60°. What is the area of the sector? (Use π = 3.14)
22. Which of the following quadrilaterals has diagonals that are equal in length and bisect each other at right angles?
23. The length of the arc of a sector is 11 cm. If the radius of the circle is 7 cm and π = 22/7, what is the angle of the sector?
24. A cone has a base radius of 5 cm and a height of 12 cm. What is the slant height of the cone?
25. What is the total surface area of a cube with an edge length of 5 cm?
26. In a cyclic quadrilateral ABCD, ∠A = 80° and ∠B = 70°. What are the measures of ∠C and ∠D?
27. Which 3D shape can be formed by joining two identical cones at their bases?
28. The curved surface area of a cylinder is 880 cm². If the height of the cylinder is 10 cm, what is its radius? (Use π = 22/7)
29. A quadrilateral has angles measuring 70°, 80°, 90°, and x°. What is the value of x?
30. If the perimeter of an equilateral triangle is 36 cm, what is the length of each side?
31. What is the number of faces of a triangular pyramid (tetrahedron)?
32. A square is inscribed in a circle of radius 5 cm. What is the length of the diagonal of the square?
33. Which of the following is a property of a parallelogram?
34. A regular polygon has an exterior angle of 40°. How many sides does it have?
35. The volume of a rectangular prism is 120 cm³. If its length is 6 cm and its width is 5 cm, what is its height?
36. Two parallel lines are intersected by a transversal. If one of the corresponding angles is 75°, what is the measure of the other corresponding angle?
37. If the hypotenuse of a right-angled triangle is 13 cm and one of the other sides is 5 cm, what is the length of the third side?
38. What is the sum of the angles around a point?
39. A circular ring has an outer radius of 10 cm and an inner radius of 8 cm. What is the area of the ring?
40. If two angles of a triangle are equal, what type of triangle is it?
41. What is the lateral surface area of a cylinder with radius 4 cm and height 7 cm? (Use π = 22/7)
42. In a triangle, if one angle is obtuse, what can be said about the other two angles?
43. What is the sum of the interior angles of a hexagon?
44. A sphere has a radius of 3 cm. What is its volume? (Use π = 3.14)

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