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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