Question

Find the area of shaded portion

Answer 1

Step-by-step explanation:

(a)

Given:- side = 21cm

and theeta = 90°

we know that, (in square all angles are of 90°)

so, by using the formula of area of sector

ar. of sector = theeta/360° × πr2

= 90°/360° × 22/7 × 21/2 × 21/2

= 1/4 × 22/7 × 21/2 × 21/2

= 693/8 cm2 similarly, area of four sector = 4 × 693/8

= 693/2 cm2

now, area of square = side × side

= 21 × 21

= 441 cm2

at last area of shaded region = area of square - area of 4 sector

= 441cm - 693/8cm

= 882/2 - 693/2

= 189/2

= 94.5 cm2

And:- therefore, the area of shaded region is 94.5cm2

(b)

Given:- R= 28 cm

r= 21 cm

area of sector with radius (R) = theeta/360° × πR2

= 90°/360° × 22/7 × 28 × 28

= 22 × 28

= 616 cm2

similarly, area of sector with radius (r) = theeta/360° × πr2

= 90°/360° × 22/7 × 21 × 21

= 693°/2 cm2

now, area of shaded region = area of sector with radius (R) - area of sector with radius (r)

= 616/1 - 693/2

= 1232/2 - 693/2

= 593/2 cm2

= 269.5 cm2

Ans:- therefore, area of shaded region is 269.5 cm2.

(c)

Given:- length of rectangle= 50cm

breath of rectangle\ diameter of circle = 14cm

so, radius= 14/2 = 7cm

Area of semi circle= 1/2 πr2

= 1/2 × 22/7 × 7× 7

= 11 × 7

= 77cm2

and, area of rectangle= length × breath

= 50cm × 14cm

= 700cm2

now,... area of shaded region = area of rectangle - area of semi circle

= 700 - 77

= 623cm2

therefore, area of shaded region is 623cm2.

hope..... this will helpful for you...