Question

In the fig. Arcs of equal radius of 14cm are drawn at each vertex of a equilateral triangle. Find the attached of shaded region

Answer 1

The attached of shaded region is 77/3 cm^2.

Consider the below figure, while following the steps.

The shaded area = sector ADE

The area of sector ADE $= \dfrac{\theta }{360^0}\pi r^2$

Given, the triangle is equilateral, hence the angle is 60°

The side of a triangle = 14 cm

The radius of each circle = Half length of side of triangle = 14/2 = 7 cm

Area of sector ADE $= \dfrac{\theta }{360^0}\pi r^2$

$= \dfrac{60}{360} \times \dfrac{22}{7} \times 7^2\\\\=\dfrac{1}{6} \times \dfrac{22}{7} \times 49\\\\=\dfrac{1}{3} \times 11 \times 7\\\\=\dfrac{77}{3}$

Area of sector = 77/3 cm^2