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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.

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 314 for n and do class=

Respuesta :

nicoleehydee
area of rectangle
7x(7x2x3)
=294

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

Answer
294-65.94
=228.06cm2
Hrishii

Step-by-step explanation:

Width of rectangle = 7 cm

[tex] \because [/tex] width of rectangle is equal to the radius of each semicircle.

[tex] \therefore [/tex] radius of each semicircle (r) = 7 cm.

[tex] \therefore [/tex] Diameter of each semicircle = 14 cm

[tex] \therefore [/tex] Length of rectangle = 3 x 14 = 42 cm.

[tex]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}}} \\ [/tex]

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