Important Questions for CBSE Class 9 Maths Chapter 8 Quadrilaterals

---

Very Short Answer Questions [1 Mark Questions]

Ques. What is a quadrilateral? Mention 6 types of quadrilaterals.

Ans: A quadrilateral is a 4 sided polygon having a closed shape. It is a 2-dimensional shape.

The 6 types of quadrilaterals include:

• Rectangle
• Square
• Parallelogram
• Rhombus
• Trapezium
• Kite

Ques. What is the base of a rhombus, if its area is 40 square units and the height is 8 units?

Ans: Given,

Area = 40 square units

Height = 8 units

Area of rhombus = Base × Height

40 = Base × 8

Base = 40/8 = 5 units

Ques. If 15 metres and 6 metres are diagonal lengths of a kite, then what is its area?

Ans: Given, diagonal 1 = 15 metres and diagonal 2 = 6 metres. So, the area is simply calculated as, (1/2)(15×6) = 45 m².

Ques. Find the perimeter of the quadrilateral with sides 5 cm, 7 cm, 9 cm and 11 cm.

Ans: Given, sides of a quadrilateral are 5 cm, 7 cm, 9 cm and 11 cm.

Therefore, the perimeter of the quadrilateral is:

P = 5 cm + 7 cm + 9 cm + 11 cm = 32 cm

Ques. Is it possible to draw a quadrilateral whose all angles are obtuse angles?

Ans: It is known that the interior angle of a quadrilateral is always 360°. Now if we have all the angles as obtuse, the angles of the quadrilateral will become greater than 360°. So practically, it is not possible to draw a quadrilateral whose all angles are obtuse angles.

Ques. If the diagonals of a parallelogram are equal, then state its name.

Ans. If the diagonals of a parallelogram are equal then it is called a rectangle.

Ques. The diagonals of which quadrilaterals are equal and bisect each other at 90°?

Ans: Square. The diagonals of a square are equal and bisect each other at 90°.

Ques. Determine the area of a parallelogram with a base of 5 cm and a height of 3 cm.

Ans. Given that the base length is 5 cm and the height is 3 cm,

Area = 5 x 3 = 15 sq.cm, according to the formula.

Also Read:

---

Short Answer Questions [2 Marks Question]

Ques. The perimeter of the quadrilateral is 50 cm and the lengths of the three sides are 9 cm, 13 cm and 17 cm. Find the missing side of the quadrilateral.

Ans: Let the unknown side of the quadrilateral = x

Given, Perimeter of the quadrilateral = 50 cm

The lengths of the other three sides are 9 cm, 13 cm and 17 cm

As we know,

Perimeter = sum of all four sides.

50 = 9 cm + 13 cm + 17 cm + x

50 = 39 + x

x = 50 – 39

x = 11

Therefore, the fourth side of the quadrilateral = 11 cm

Ques. How do you calculate the perimeter of a quadrilateral with sides of 2 cm, 7 cm, 9 cm, and 10 cm?

Ans. The perimeter of a quadrilateral is calculated by adding the lengths of all four sides.

The lengths of a quadrilateral's four sides are 2 cm, 7 cm, 9 cm, and 10 cm.

Quadrilateral perimeter = 2 cm + 7 cm + 9 cm + 10 cm = 28 cm

Ques. Find the fourth angle of a quadrilateral whose angles are 90°, 45° and 60°.

Ans: By the angle sum property we know;

Sum of all the interior angles of a quadrilateral = 360°

Let the unknown angle be x

So,

90° + 45° + 60° + x = 360°

195° + x = 360°

x = 360° – 195°

x = 165°

Ques. In a trapezium ABCD,. Calculate ∠C and ∠D if ∠A = 55° and ∠B = 70°

Ans: In a trapezium ABCD, ∠A + ∠D = 180° and ∠B + ∠C = 180°

So, 55° + ∠D = 180°

Or, ∠D = 125°

Similarly,

70° + ∠C = 180°

Or, ∠C = 110°

Ques. Calculate all the angles of a parallelogram if one of its angles is twice its adjacent angle.

Ans: Let the angle of the parallelogram given in the question statement be “x”.

Now, its adjacent angle will be 2x.

It is known that the opposite angles of a parallelogram are equal.

So, all the angles of a parallelogram will be x, 2x, x, and 2x

As the sum of interior angles of a parallelogram = 360°,

x + 2x + x + 2x = 360°

Or, x = 60°

Thus, all the angles will be 60°, 120°, 60°, and 120°.

Ques. Identify the type of quadrilaterals:

(i) The quadrilateral is formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are perpendicular.

(ii) The quadrilateral is formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are congruent.

Ans:

(i) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are perpendicular is a rectangle.

(ii) The quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are congruent is a rhombus.

Read Also:

---

Short Answer Questions [3 Marks Question]

Ques. Using the length and height of the trapezoid's bases, calculate its area. You have a trapezoid with an 8-cm base and a 12-cm base, and a 4-cm-long height line connecting them.

Ans. The formula based on the trapezoid's length and the heights of both bases will be used in the given question:

Height = Area = Base1+Base2/2

or

A = (m + n) / 2 × h

By using the above equation.

Its area can be calculated as follows: (8 + 12)/2 x 4 = (20)/2 x 4 = 40cm

Ques. The following measurements can be used to calculate the area of a kite. What is the area of the kite if its diagonals are 18 metres and 6 metres long?

Ans. As we know that a rhombus represents a equal length, we'll use the rhombus diagonal formula to calculate its area.

Use the rhombus diagonal formula:-

(Diag. 1 Diag. 2)/2 = Area

We obtain (18 x 6) / 2 as a result.

54 square metres = 108/2

Straight-line segments on the kite that run between two opposed corners are called diagonals.

Ques. Find all the angles of a parallelogram if one angle is 80°.

Ans: For a parallelogram ABCD, opposite angles are equal.

So, the angles opposite to the given 80° angle will also be 80°.

It is also known to us that the sum of angles of any quadrilateral = 360°.

So, if ∠A = ∠C = 80° then,

∠A + ∠B + ∠C + ∠D = 360°

Also, ∠B = ∠D

Thus,

80° + ∠B + 80° + ∠D = 360°

Or, ∠B +∠ D = 200°

Hence, ∠B = ∠D = 100°

Now, we have all the angles of the quadrilateral that are as follows:

∠A = 80°

∠B = 100°

∠C = 80°

∠D = 100°

Ques.Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each of the equal angles of the quadrilateral.

Ans: The measure of equal angles of a quadrilateral is 72°.

As we know that in a quadrilateral ABCD having interior angles, angle a, angle b, angle c and angle d, the sum of four interior angles is equal to 360°.

This means,

angle a + angle b + angle c + angle d = 360°

Now, as given, we have,

Three angles of a quadrilateral are equal.

The fourth angle of a quadrilateral = 144°.

So,

let x be the measure of equal angles.

∴ x + x + x + 144° = 360°

Thus,

⇒ 3x + 144° = 360°

⇒ 3x = 360° - 144° 

⇒ 3x = 216°  

⇒ x = 72°  

Hence, the equal angles of a quadrilateral are equal to 72°.

Also check: 

---

Long Answer Questions [5 Marks Question]

Ques. Prove that the angle bisectors of a parallelogram form a rectangle.

Ans:

LMNO is a parallelogram in which bisectors of the angles L, M, N, and O intersect at P, Q, R and S to form the quadrilateral PQRS.

LM || NO (opposite sides of parallelogram LMNO)

L + M = 180 (sum of consecutive interior angles is 180o)

MLS + LMS = 90

In LMS, MLS + LMS + LSM = 180

90 + LSM = 180

LSM = 90

RSP = 90 (vertically opposite angles)

SRQ = 90, RQP = 90 and SPQ = 90

Therefore, PQRS is a rectangle.

Ques. Calculate all the angles of a quadrilateral if they are in the ratio 2:5:4:1.

Ans:

As the angles are in the ratio 2:5:4:1, they can be written as-

2x, 5x, 4x, and x

Now, as the sum of the angles of a quadrilateral is 360°,

2x + 5x + 4x + x = 360°

Or, x = 30°

Now, all the angles will be,

2x =2 × 30° = 60°

5x = 5 × 30° = 150°

4x = 4 × 30° = 120°, and

x = 30°

Ques. In a rectangle, one diagonal is inclined to one of its sides at 25°. Measure the acute angle between the two diagonals.

Ans:

Let ABCD be a rectangle where AC and BD are the two diagonals which are intersecting at point O.

Now, assume ∠BDC = 25° (given)

Now, ∠BDA = 90° – 25° = 65°

Also, ∠DAC = ∠BDA, (as diagonals of a rectangle divide the rectangle into two congruent right triangles)

So, ∠BOA = the acute angle between the two diagonals = 180° – 65° – 65° = 50°

Related links: