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

Step-by-step 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.

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