Question

Three semicircles are placed in a rectangle, as shown below. The width of the 3 rectangle is 15 . Find the area of the shaded region. Use the value 3.14 of pie , and do not round your answer.

Answer 1

Explanation:

Width of rectangle = 15 cm

width of rectangle is equal to the radius of each semicircle.

radius of each semicircle (r) = 15 cm.

Diameter of each semicircle = 30 cm

Length of rectangle = 3 x 30 = 90 cm.

`Area \: of \: shaded \: region \\ = Area \: of \: rectangle \\ \: \: \: \: \: - 3 * area \: of \: one \: semicircle \\ = l * w - 3 * \frac{\pi {r}^(2) }{2} \\ \\ = 90 * 15 - 3 * \frac{3.14 * {15}^(2) }{2} \\ \\ = 1350 - 3 * (3.14 * 225 )/(2) \\ \\ = 1350 - (2119.5)/(2) \\ \\ = 1350 - 1059.75 \\ \\ \purple { \boxed{ \therefore \: Area \: of \: shaded \: region = 290.25 \: {cm}^(2)}} \\`