Question

In a semi circle AC = BD = 7 cm and AB = CD = 1.75 cm . Find the shaded region​

Answer 1

Given:-

▪︎AC = BD

▪︎AC = 7 cm , BD = 7 cm

▪︎AB = CD

▪︎AB = 1.75 cm , CD = 1.75 cm

To Find:-

▪︎Shaded region of the Semi circle

Solution:-

▪︎Here they given that AC and BD are equal and their value is 7 cm and AB and CD are equal and their value is 1.75 cm.

▪︎To find the shaded region of the Semi circle, Using formula.

$\star { \underline{ \boxed{ \sf{} = 2 \left(Area \: of \:the \: semi \: circle \: of \: radius \: \frac{7}{2} \: cm \right) -2 \left(Area \: of \:the \: semi \: circle \: of \: radius \: \frac{7}{8} \: cm \right) }}} \star$

$\\ \longrightarrow \tt \: 2 \left( \frac{1}{2} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \right) - 2\left( \frac{1}{2} \times \frac{22}{7} \times \frac{7}{4} \times \frac{7}{4} \right)$

$\\ \longrightarrow \tt\left( \frac{77}{2} - \frac{77}{8} \right)$

$\\ \longrightarrow \tt \frac{77}{2} \left(1 - \frac{1}{4} \right)$

$\\ \longrightarrow \tt \frac{77}{2} \times \frac{3}{4}$

$\\ \longrightarrow \tt \frac{231}{8}$

$\\ \tt { = 28.87 \: {cm}^{2} }$

▪︎Hence, The area of the shaded region of the Semi circle is 28.87 cm²