Question

The figure shows a quarter circle and an equilateral triangle. What is thearea of the shaded part? Give your answer to 3 significant figures. (Take it= 3.14.)=7 cmYour answer

Answer 1

Explanation

The shaded area represents a segment. This can be solved with the formula below;

$\mleft(\frac{\theta}{360}\mright)\times\pi r^2-\frac{1}{2}r^2sin\theta$

Since the triangle is an equilateral triangle, it implies that the angle subtended at the centre is 60 degrees. Also, the given radius is 7 cm

$\begin{gathered} =7^2(\frac{60}{360}\times3.14-\frac{1}{2}\times\sin 60)^{}_{} \\ =49(\frac{3.14}{6}-\frac{\sqrt[]{3}}{4}) \\ =4.43\operatorname{cm}^2 \end{gathered}$

Answer:

$4..43\operatorname{cm}^2$