Question

Find the perimeter and area of the shaded region shown in the figure. The four corners are circle quadrants and at the centre, there is a circle.
[Take $\pi =3.14$]

• A. Perimeter = 20.56 cm
• B. Area = 9.72 $c{m}^2$
• C. Area = 20.56 $c{m}^2$
• D. Perimeter = 9.72 cm

Answer 1

Answer: (A), (B)

The correct options are
A Perimeter = 20.56 cm
B Area = 9.72 $c{m}^2$

Area of square $=Sid{e}^2=4^2=16c{m}^2$
Area of cut portion = Area of two circles = 1 circle + 4quadrants
$=2\times pi\times 1^2$
$=6.28c{m}^2$
So, area of remaining portion of square $=(16-6.28)=9.72c{m}^2$
Perimeter of the shaded region =4 quadrant + 1 circle+portion of the square
$=4\times \frac{2\pi r}{4}+2\pi r+4\left(2\right)$
$=4\times \frac{2\pi \left(1\right)}{4}+2\pi \left(1\right)+8$
$=4\pi +8$
$=20.56cm$