Question 513 Marks
A child makes a poster on a chart paper drawing a square ABCD of side 14cm. 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.$\Big(\text{Use }\pi=\frac{22}{7}\Big)$
Answer
View full question & answer→Radius of circular arc (r) = 7cm Side of square ABCD (a) = 14cm
Area of shaded region
= Area of square - 4 × Area of quadrant $=(\text{a})^2-4\times\frac{1}{4}\pi\text{r}^2$ $=(14)^2-\frac{22}{7}\times7\times7\text{cm}^2$ $=196-154=42\text{cm}^2$ Perimeter = 4 × Perimeter of arc of quadrant $=4\times\frac{1}{4}(2\pi\text{r})$ $=2\times\frac{22}{7}\times7=44\text{cm}$
Area of shaded region= Area of square - 4 × Area of quadrant $=(\text{a})^2-4\times\frac{1}{4}\pi\text{r}^2$ $=(14)^2-\frac{22}{7}\times7\times7\text{cm}^2$ $=196-154=42\text{cm}^2$ Perimeter = 4 × Perimeter of arc of quadrant $=4\times\frac{1}{4}(2\pi\text{r})$ $=2\times\frac{22}{7}\times7=44\text{cm}$