Quadrilaterals & Special Quadrilaterals Quiz - ICSE Class 8 Mathematics

Free practice quiz: Quadrilaterals & Special Quadrilaterals (ICSE Class 8 Mathematics). 42 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 8 Mathematics practice quiz has 42 multiple-choice questions on Quadrilaterals & Special Quadrilaterals, and 42 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. In a parallelogram ABCD, if $\angle A = 70^\circ$, then the measure of $\angle B$ is:

   1. $70^\circ$
   2. $110^\circ$
   3. $90^\circ$
   4. $180^\circ$
   Show answer

   Answer: B. $110^\circ$

   In a parallelogram, consecutive angles are supplementary. Therefore, $\angle A + \angle B = 180^\circ$. Given $\angle A = 70^\circ$, we have $70^\circ + \angle B = 180^\circ$, which means $\angle B = 180^\circ - 70^\circ = 110^\circ$.

2. A kite has diagonals of length 8 cm and 6 cm. What is its area?

   1. $24$ cm$^2$
   2. $48$ cm$^2$
   3. $14$ cm$^2$
   4. $28$ cm$^2$
   Show answer

   Answer: A. $24$ cm$^2$

   The area of a kite is given by the formula $\frac{1}{2} imes d_1 imes d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. Here, $d_1 = 8$ cm and $d_2 = 6$ cm. So, Area = $\frac{1}{2} imes 8 imes 6 = \frac{1}{2} imes 48 = 24$ cm$^2$.

3. If a parallelogram has diagonals that are equal in length and bisect each other at right angles, then the parallelogram must be a:

   1. Rectangle
   2. Rhombus
   3. Square
   4. Kite
   Show answer

   Answer: C. Square

   A parallelogram with equal diagonals is a rectangle. A parallelogram with diagonals that bisect each other at right angles is a rhombus. A parallelogram that is both a rectangle and a rhombus is a square. Therefore, a parallelogram with diagonals that are equal, bisect each other, and are perpendicular must be a square.

4. A quadrilateral ABCD has angles $\angle A = 90^\circ$, $\angle B = 90^\circ$, $\angle C = 120^\circ$, and $\angle D = 60^\circ$. This quadrilateral is a:

   1. Rectangle
   2. Rhombus
   3. Trapezoid
   4. Square
   Show answer

   Answer: C. Trapezoid

   The sum of interior angles is $90^\circ + 90^\circ + 120^\circ + 60^\circ = 360^\circ$, which is correct for a quadrilateral. For it to be a trapezoid, at least one pair of opposite sides must be parallel. If $\angle B = 90^\circ$ and $\angle C = 120^\circ$, then $\angle B + \angle C = 210^\circ$, so BC is not parallel to AD. If $\angle A = 90^\circ$ and $\angle D = 60^\circ$, then $\angle A + \angle D = 150^\circ$, so AB is not parallel to DC. However, if $\angle A = 90^\circ$ and $\angle B = 90^\circ$, this means that AD is parallel to BC because the angles on the same leg (AB) are supplementary (which is not the case here, $90+90=180$). Wait, angles on the same leg being supplementary implies the other two sides are parallel. If $\angle A = 90^\circ$ and $\angle B = 90^\circ$, then AD is parallel to BC. Therefore, it is a trapezoid. It is not a rectangle because $\angle C$ and $\angle D$ are not $90^\circ$. It is not a rhombus because not all sides are necessarily equal, and angles are not all equal. It is not a square as it's not a rectangle with equal sides.

5. What is the sum of the interior angles of a quadrilateral formed by joining the midpoints of the sides of a larger square?

   1. $180^\circ$
   2. $360^\circ$
   3. $270^\circ$
   4. $90^\circ$
   Show answer

   Answer: B. $360^\circ$

   Connecting the midpoints of the sides of a square forms another square inside it. Let the vertices of the outer square be (0,a), (a,a), (a,0), (0,0). The midpoints are (a/2, a), (a, a/2), (a/2, 0), (0, a/2). These four midpoints form a square. A square is a quadrilateral. The sum of the interior angles of any quadrilateral is $360^\circ$.

More questions in this quiz

Answers and explanations are in the full quiz.

1. A rectangle has a length of 12 cm and a breadth of 5 cm. What is its perimeter?
2. The diagonals of a rhombus are perpendicular bisectors of each other. If one diagonal is 10 cm and the other is 24 cm, what is the length of each side of the rhombus?
3. Which of the following quadrilaterals has all sides equal and all angles equal?
4. The sum of the interior angles of a quadrilateral is:
5. If two adjacent angles of a parallelogram are in the ratio $1:2$, what are the measures of the angles?
6. Which of the following is NOT a property of a rectangle?
7. In a trapezoid ABCD, AB is parallel to DC. If $\angle D = 110^\circ$ and $\angle C = 70^\circ$, then $\angle A + \angle B$ is:
8. In an isosceles trapezoid, the base angles are equal. If one of the base angles is $115^\circ$, what is the measure of the adjacent angle on the other base?
9. The perimeter of a square is 48 cm. What is the length of its diagonal?
10. Which quadrilateral has diagonals that are equal, perpendicular, and bisect each other?
11. In a parallelogram ABCD, $\angle A = 5x - 10^\circ$ and $\angle B = 3x + 30^\circ$. Find the measure of $\angle A$.
12. What is the measure of each interior angle of a regular octagon?
13. In a cyclic quadrilateral ABCD, if $\angle A = 80^\circ$, then the measure of $\angle C$ is:
14. The sum of the exterior angles of any convex polygon is:
15. A quadrilateral has interior angles measuring $x^\circ$, $2x^\circ$, $3x^\circ$, and $4x^\circ$. Find the value of $x$.
16. In a rhombus ABCD, $\angle ABC = 130^\circ$. What is the measure of $\angle BAD$?
17. A rectangle has an area of 72 cm$^2$ and a length of 9 cm. What is its perimeter?
18. Which of the following quadrilaterals has diagonals that are always perpendicular bisectors of each other?
19. If the sum of two opposite angles of a parallelogram is $200^\circ$, then the measure of each of the other two opposite angles is:
20. The area of a rhombus is 150 cm$^2$. If the length of one of its diagonals is 20 cm, find the length of the other diagonal.
21. In an isosceles trapezoid, the non-parallel sides are equal in length. If the lengths of the parallel sides are 10 cm and 16 cm, and the height is 5 cm, what is the perimeter?
22. In a parallelogram ABCD, the diagonals intersect at point O. If $AO = 5$ cm and $BO = 7$ cm, then what are the lengths of AC and BD?
23. In a kite ABCD, AB = AD and CB = CD. If $\angle ABC = 110^\circ$, what is the measure of $\angle ADC$?
24. The sum of the interior angles of a pentagon is:
25. If a rhombus has an angle of $60^\circ$, then the other three angles are:
26. Which property is true for a parallelogram but not necessarily for a rhombus?
27. In a cyclic quadrilateral ABCD, $\angle A = 75^\circ$ and $\angle B = 85^\circ$. Find $\angle C$ and $\angle D$.
28. The perimeter of a rectangle is 50 cm. If its length is 15 cm, what is its area?
29. A quadrilateral with all sides equal and diagonals that are perpendicular bisectors of each other is a:
30. In a trapezoid, if the non-parallel sides are equal, it is called a/an:
31. If a parallelogram has diagonals of lengths 10 cm and 24 cm that bisect each other at right angles, what is the length of a side of the parallelogram?
32. Which of the following is a property of a cyclic quadrilateral?
33. The area of a square is 81 cm$^2$. What is the length of its diagonal?
34. In a parallelogram ABCD, $\angle A = 85^\circ$. What is the measure of $\angle C$?
35. The area of a quadrilateral is the sum of the areas of the two triangles formed by drawing one of its diagonals. This statement is:
36. A quadrilateral has sides in ratio $2:3:4:5$. If the sum of the interior angles is $360^\circ$, this does not uniquely determine the type of quadrilateral. However, if the largest angle is $150^\circ$, what is the value of the smallest angle?
37. In a parallelogram ABCD, if $\angle ADB = 30^\circ$ and $\angle ABD = 70^\circ$, then $\angle BCD$ is:

More quizzes

• Ratio and Proportion▶ Play
• Rational Numbers▶ Play
• Relations and Functions▶ Play
• Representing 3D in 2D▶ Play
• Sets▶ Play
• Simple and Compound Interest▶ Play

Browse all Mathematics quizzes

More to play