Question

Three semicircles are placed in a rectangle as shown below. The width of the rectangle is 7 cm.

Find the area of the shaded region. Use the value 3.14 for n, and do not round your answer.
Be sure to include the correct unit in your answer.

Answer 1

area of rectangle
7x(7x2x3)
=294

area of 3 semicircles
7x2x3.14x0.5x3
=65.94

Answer
294-65.94
=228.06cm2

Answer 2

Explanation:

Width of rectangle = 7 cm

`\because` width of rectangle is equal to the radius of each semicircle.

`\therefore` radius of each semicircle (r) = 7 cm.

`\therefore` Diameter of each semicircle = 14 cm

`\therefore` Length of rectangle = 3 x 14 = 42 cm.

`Area \: of \: shaded \: region \\ = Area \: of \: rectangle \\ \: \: \: \: \: - 3 * area \: of \: one \: semicircle \\ = l * w - 3 * \frac{\pi {r}^(2) }{2} \\ \\ = 42 * 7 - 3 * \frac{3.14 * {7}^(2) }{2} \\ \\ = 294 - 3 * (3.14 * 49 )/(2) \\ \\ = 294 - (461.58)/(2) \\ \\ = 294 - 230.79 \\ \\ \purple { \boxed{ \therefore \: Area \: of \: shaded \: region = 63.21 \: {cm}^(2)}} \\`