Question

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles (in the following figure). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region.
(Use π = 22/7)

 

Answer 1

Perimeter of the shaded portion = 4 ⨯ Length of the arc having central angle 90^∘ 

^{\[= 4 \times \frac{90°}{360°} \times 2 \times \frac{22}{7} \times \frac{14}{2}\]
\[ = 4 \times \frac{1}{4} \times 2 \times \frac{22}{7} \times 7\]
\[ = 44 cm\]}

^{Area of shaded portion = Area of square ABCD − 4 ⨯ Area of the arc having central angle 90∘} 

^{\[= \left( 14 \right)^2 - 4 \times \frac{90°}{360°} \times \frac{22}{7} \times \left( \frac{14}{2} \right)^2 \]
\[ = 196 - 4 \times \frac{1}{4} \times \frac{22}{7} \times \left( 7 \right)^2 \]
\[ = 196 - 154\]
\[ = 42 {cm}^2\]}