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^∘
$$\begin{gathered} =4\times \frac{90°}{360°}\times 2\times \frac{22}{7}\times \frac{14}{2} \\ =4\times \frac{1}{4}\times 2\times \frac{22}{7}\times 7 \\ =44\mathrm{cm} \end{gathered}$$
Area of shaded portion = Area of square ABCD − 4 ⨯ Area of the arc having central angle 90^∘
$$\begin{gathered} ={\left(14\right)}^2-4\times \frac{90°}{360°}\times \frac{22}{7}\times {\left(\frac{14}{2}\right)}^2 \\ =196-4\times \frac{1}{4}\times \frac{22}{7}\times {\left(7\right)}^2 \\ =196-154 \\ =42{\mathrm{cm}}^2 \end{gathered}$$