Understanding Quadrilaterals Class 8 Worksheet Maths Chapter 3

Multiple Choice Questions (MCQs)

Q1: What is the number of diagonals in a 6-sided polygon?

A) 6
B) 7
C) 9
D) 10

Ans: (C)

Explanation: The number of diagonals in an n-sided polygon is given by n(n − 3)/2. For n = 6, diagonals = 6 × (6 − 3)/2 = 6 × 3/2 = 9. Hence option (C) is correct.

Q2: What will be the sum of interior angles of a polygon having 8 sides?

A) 720°
B) 1080°
C) 1260°
D) 1440°

Ans: (B)

Explanation: Sum of interior angles of an n-sided polygon = (n − 2) × 180°. For n = 8, sum = (8 − 2) × 180° = 6 × 180° = 1080°. Hence option (B) is correct.

Q3: Find out the number of sides of a regular polygon whose exterior angles are 60°.

A) 3
B) 4
C) 6
D) 12

Ans: (C)

Explanation: The sum of exterior angles of any polygon is 360°. If each exterior angle is 60°, number of sides = 360°/60° = 6. Hence (C).

Q4: The sides of a quadrilateral are in the ratio of 2:5:4:1. Find out the sum of the smallest and largest angles.

A) 120°
B) 180°
C) 240°
D) 360°

Ans: (B)

Explanation: If we assume the angles are in the same ratio as the given numbers, let the angles be 2x, 5x, 4x and 1x. Then 2x + 5x + 4x + 1x = 12x = 360° so x = 30°. The smallest angle = 1x = 30° and the largest = 5x = 150°. Their sum = 30° + 150° = 180°. Hence (B).

Q5: If the area of a square field is 144 sq m, then find the perimeter.

A) 24 m
B) 36 m
C) 48 m
D) 60 m

Ans: (C)

Explanation: If area = 144 sq m, side length = √144 = 12 m. Perimeter = 4 × side = 4 × 12 = 48 m. Hence (C).

Q6: If the base of a triangle is 3 cm and the height is 6 cm, then find the area.

A) 6 sq cm
B) 9 sq cm
C) 12 sq cm
D) 18 sq cm

Ans: (B)

Explanation: Area of a triangle = 1/2 × base × height = 1/2 × 3 cm × 6 cm = 9 sq cm. Hence (B).

Q7: A square field has a diagonal of 8 m. Then find out the area of the field.

A) 32 sq m
B) 48 sq m
C) 64 sq m
D) 128 sq m

Ans: (A)

Explanation: For a square with diagonal d, side = d/√2. Here side = 8/√2 = 4√2 m. Area = side2 = (4√2)2 = 16 × 2 = 32 sq m. Hence (A).

True/False

Q1: The sum of interior angles of a polygon having 8 sides is 1080°. 

Ans: True

Explanation: Sum = (n − 2) × 180°. For n = 8, (8 − 2) × 180° = 1080°, so the statement is true.

Q2: A regular polygon with exterior angles of 60° has 6 sides. 

Ans: True

Explanation: Number of sides = 360°/exterior angle = 360°/60° = 6. So the statement is true.

Q3: The sum of the smallest and largest angles of a quadrilateral, with sides in the ratio 2:5:4:1, is 240°. 

Ans: False

Explanation: If angles are taken in the ratio 2:5:4:1, then one part x = 30° (since total 12x = 360°). Smallest = 30°, largest = 150°; sum = 180°, not 240°. Hence the statement is false.

Q4: The perimeter of a square field, with an area of 144 sq m, is 48 m. 

Ans: True

Explanation: Side = √144 = 12 m; perimeter = 4 × 12 = 48 m. Statement is true.

Q5: The area of a triangle with a base of 3 cm and height of 6 cm is 9 sq cm. 

Ans: True

Explanation: Area = 1/2 × base × height = 1/2 × 3 × 6 = 9 sq cm. Statement is true.

Q6: A square field with a diagonal of 8 m has an area of 32 sq m. 

Ans: True

Explanation: Side = 8/√2 = 4√2 m; area = (4√2)2 = 32 sq m. Statement is true.

Very Short Answer Questions

Q1: Write down the formula of area of rhombus.

Ans: 1⁄2 × product of diagonals

Q2:  Can all the angles of a quadrilateral be right angles?

Ans: Yes, all the angles of a quadrilateral can be right angles.

Q3:  Name the quadrilateral whose diagonals are equal.

Ans: Rectangle, Square

Q4: Each angle of a square measures ___°.

Ans: 90°

Q5: How many parallel lines are in a trapezium?

Ans: 2

Q6: Which figure is equiangular and equilateral polygons?

Ans: Square

Q7: It rhombus also satisfied the properties of a_______.

Ans: Parallelogram

Q8: If the diagonals of a quadrilateral are perpendicular bisectors of each other then it is always a______.

Ans: Rhombus

Q9: the sum of all angles in a quadrilateral is equal to_____ right angles.

Ans: 4

Short Answer Questions

Q1: A room has a length of 10 m, breadth of 5m and height of 8 m. Find out the area of the room.

Ans: Floor area = length × breadth = 10 m × 5 m = 50 sq m.
Note: If the question meant wall area (lateral surface area) or total surface area, different formulas apply. Here we have given the floor area as the usual meaning of "area of the room".

Q2: The length of one side of a rhombus is 6.5 centimeters and its altitude is 10 centimeter. if the length of one side of its diagonals is 26 centimeter find the length of the other diagonal.

Ans: Area = base × altitude = 6.5 cm × 10 cm = 65 sq cm.
Area also = 1⁄2 × (d1 × d2). Given d1 = 26 cm and let d2 = x cm.
So, 1⁄2 × 26 × x = 65
⇒ 13x = 65
⇒ x = 5 cm.
Remark: With these diagonals the side calculated from diagonals would be √[(26/2)2 + (5/2)2] ≈ 13.24 cm, which does not match the given side 6.5 cm. The numerical answer for the other diagonal from the area relation is 5 cm, but the given data are inconsistent for a rhombus.

Q3: If three angles of a trapezium is 50°, 130° and 120°. Then find the other angle.

Ans: Other angle = 360° − (50° + 130° + 120°) = 360° − 300° = 60°.

Q4: If two adjacent angles of a parallelogram are in the ratio 2:3 Find all the angles of the parallelogram.

Ans: Let the adjacent angles be 2x and 3x.
Since adjacent angles in a parallelogram are supplementary: 2x + 3x = 180° ⇒ 5x = 180° ⇒ x = 36°.
Thus angles are 2x = 72° and 3x = 108°. Opposite angles are equal, so the four angles are 72°, 108°, 72°, 108°.

Q5: if the angles of a quadrilateral are in the ratio 3:6:8:13. The largest angle is?

Ans: Sum of parts = 3 + 6 + 8 + 13 = 30 parts.
Each part = 360°/30 = 12°.
Largest angle = 13 × 12° = 156°.

Q6: diagonals of a quadrilateral ABCD bisect each other. If A=45°. Then B=?

Ans: If the diagonals bisect each other, the quadrilateral is a parallelogram. Adjacent angles in a parallelogram are supplementary.
So A + B = 180° ⇒ 45° + B = 180° ⇒ B = 135°.

Q7: The angles of a quadrilateral are x°, x+5°, x+10°, x+25°. Then find the value of x.

Ans: x + (x + 5) + (x + 10) + (x + 25) = 360°
4x + 40 = 360° ⇒ 4x = 320° ⇒ x = 80°.