Question

Help me on calculating the area of the shaded part

Answer 1

Answer:

1053.50 mm^2

Explanation:

first calculate the area of square ABCD

area of ABCD = AB × AB

= 70 × 70 = 4900 mm^2

if you look closely, there are 4 quater-circles with radius (AB/2 = 35 mm) and their center A,B,C and D.

now

area of any one quater circle =( pi × r^2 )/4

area of 4 quater circle =(pi × r^2)

where, pi = 3.14 and r = radius of quater circle

area of 4 quater-circle = (3.14 × 35^2)= 3846.50 mm^2

hence area of shaded region = area of square - area of 4 quater circles

= 4900 - 3846.50

=1053.50 mm^2

Answer 2

`1051 .55 {mm}^(2)`

Explanation:

Find the area of the square - area of 4 sectors

We'll use the formula to find one sector area

`a = (1)/(2) * {r}^(2) * x`

where r is the radius of one sector and x is the angle in radians

Since each angle is in a square, the angle of the sectors is 90 degrees.

Convert degrees to radians

`90 = (1)/(2) \pi \: rad`

The radius of one sector is given by 70mm/2=35mm

One sector area:

`(1)/(2) * {35}^(2) * (1)/(2) \pi = 306.25\pi`

Area of all 4 sectors:

`4 * 306.25\pi = 1225\pi`

Area of the square:

`70 * 70 = 4900`

Hence, Area of square - 4 Sectors:

`4900 - 1225\pi = 1051.55 {mm}^(2) (2dp)`