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# ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in Fig. 9.69. Find the area of shaded portion.

**Solution:**

Given, ABCD is a rectangle with length 80 cm and breadth 60 cm.

P, Q, R and S are the midpoints of AB, BC, CD, and DA respectively.

A circular rangoli of radius 10 cm is drawn at the centre.

We have to find the area of the shaded portion.

__Area of rectangle__ ABCD = length × breadth

= 80(60)

= 4800 cm²

The triangles SAP, PBQ, RCQ and RDS are congruent

S is the midpoint of DA

So, AS = 60/2 = 30 cm

P is the midpoint of AB

So, AP = 80/2 = 40 cm

__Area of triangle__ = 1/2 × base × height

Area of triangle SAP = 1/2 × AP × AS

= 1/2 × 40 × 30

= 20(30)

= 600 cm²

Area of 4 congruent triangles = 4(600)

= 2400 cm²

Area of rectangle PQRS = area of rectangle ABCD - area of 4 congruent triangles

= 4800 - 2400

= 2400 cm²

Area of circle = πr²

Area of circular rangoli = (3.14)(10)²

= 3.14(100)

= 314 cm²

Area of shaded portion = area of rectangle PQRS - area of circular rangoli

= 2400 - 314

= 2086 cm²

Therefore, the area of the shaded portion is 2086 cm².

**✦ Try This:** Area of the shaded portion is

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 11

**NCERT Exemplar Class 7 Maths Chapter 9 Problem 127**

## ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in Fig. 9.69. Find the area of shaded portion.

**Summary:**

ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in Fig. 9.69. The area of the shaded portion is 2086 cm².

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