Question

find the area and the perimeter of the shaded part of the following figures​

Answer 1

Answer :

1) Area = 174.8cm² & perimeter = 64cm

2) Area = 420cm² & perimeter = 104cm

Step-by-step explanation:

1) The figure is formed by adding 4 equilateral triangles on the four sides of a square of each side = 8 cm.

Area of Shaded portion = Area of square + Area of 4 equilateral triangles

= (8)² + √3 /4 × (8)² x 4 cm

= 64 + √3 x 64

= 64 + 64 × 1.73

= 64 + 110.73 = 174.73 = 174.8 cm²

and perimeter = 8 x 8 = 64 cm

2) The given figure is formed by a rectangle and semicircles side of rectangle = 30 cm and diameter of semicircle = 14 cm and breadth of rectangle = 14 cm

(a) :. Area of shaded portion = Area of rectangle + Area of a semicircle –

Area of semicircle

= Area of rectangle

= Length × Breadth = 30 × 14 = 420 cm²

(b) Perimeter = Length x 2 + Perimeter of semicircles

= 30 × 2 + 1/2 × 2πr × 2

= 30 × 2 + 2 × 22/7 × 7 --------- ( r = 14/2 = 7 )

= 60 + 44 = 104 cm