Find the area of the shaded portion in figure 6.
Solution:
The area of the shaded portion is = Area of the circle minus the area of the unshaded square and four unshaded triangles
Since the triangles are formed on the sides of the square and they are symmetrical about the horizontal and vertical axis passing through the centre of the circle it can be said that all the four triangles are equal.
Since the height of the triangle is given as 7cm the area of the triangle is given as:
Area of each triangle = 1/2 × 7 × 7 [Area of triangle = 1/2 × Base × Height]
= 49/2cm²
Area of four triangles = 4 × 49/2 = 98cm²
Area of unshaded square = 7 × 7 = 49cm²
Area of the circle = πr²
The radius of the circle = 7 + 3.5 = 10.5cm
Area of the circle = π(10.5)(10.5) = 346.50cm²
The area of the shaded region = 346.5 - 49 - 98 = 199.5 cmcm²
✦ Try This: Find the area of the shaded portion.
The area of the shaded portion is = Area of the circle minus the area of the unshaded square and four unshaded triangles
Since the triangles are formed on the sides of the square and they are symmetrical about the horizontal and vertical axis passing through the centre of the circle it can be said that all the four triangles are equal.
Since the height of the triangle is given as 14cm the area of the triangle is given as:
Area of each triangle = 1/2 × 14 × 14 [Area of triangle = 1/2 × Base × Height]
= 98cm²
Area of four triangles = 4 × 98 =392cm²
Area of unshaded square = 14 × 14 = 196cm²
Area of the circle = πr²
The radius of the circle = 14 + 7 = 21cm
Area of the circle = π(21)(21) = 1386cm²
The area of the shaded region = 1386 - 196 - 392 = 798cm²
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 83
Find the area of the shaded portion in figure 6.
Summary:
The area of the shaded portion is 199.5cm²
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