Question

In the following, ABCD is a square of side 10 cm. A sector of radius 5 cm is cut out from one of the corners. Find the area of the shaded region. (Take π = 3.14)

Answer 1

Given:

ABCD is a square, side = 10 cm.

A sector of radius 5 cm (center at A) and angle 90° is cut out.

Take π = 3.14.

Step-wise calculation:

1. Area of square = side² 

= 10²

= 100 cm²

2. Area of the sector (quarter circle):

Sector area = `(90^circ/360^circ) xx π xx r^2` 

= `(1/4) xx π xx 5^2`

= `(25π)/4 cm^2`

= 6.25π cm²

Substitute π = 3.14:

6.25 × 3.14 = 19.625 cm²

3. Shaded area = Area of square – Area of sector 

= 100 – 19.625

= 80.375 cm²

Shaded area = `100 - (25π)/4 cm^2`

= 80.375 cm² (≈ 80.38 cm²)