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19 votes
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]

User John Blakie
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1 Answer

18 votes
18 votes

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-(22)/(7)\cdot21^2 \\ A=378cm2 \end{gathered}

The answer is 378 cm2

User ThePedestrian
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