Question

6. (a) The diagram, not drawn to scale, shows a circle that fits exactly into the square ABCD as shown below. The radius of the circle is 21 cm 도 A B. 21 cm e D c Show that the area of the square is 1764 em [2] 22 Given that determine the area of the shaded region [3]

Answer 1

Part 1

Determine the area of the square

The area of the square is

$A=b^2$

where

b is the length side of the square

In this problem, the value of b is equal to the diameter of the circle

so

b=2(21)=42 cm

$\begin{gathered} A=42^2 \\ A=1,764cm2 \end{gathered}$

Part 2

Find out the area of the shaded region

The area of the shaded region is equal to the area of the square minus the area of the circle

so

$A=1,764-\pi\cdot r^2$

we have

pi=22/7

r=21 cm

substitute

$\begin{gathered} A=1,764-\frac{22}{7}\cdot21^2 \\ A=378cm2 \end{gathered}$

The answer is 378 cm2