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

Answer:

$1051 .55 {mm}^{2}$

Step-by-step explanation:

Find the area of the square - area of 4 sectors

We'll use the formula to find one sector area

$a = \frac{1}{2} \times {r}^{2} \times x$

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

$90 = \frac{1}{2} \pi \: rad$

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

One sector area:

$\frac{1}{2} \times {35}^{2} \times \frac{1}{2} \pi = 306.25\pi$

Area of all 4 sectors:

$4 \times 306.25\pi = 1225\pi$

Area of the square:

$70 \times 70 = 4900$

Hence, Area of square - 4 Sectors:

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