3 years ago

Landon used a semicircle, a rectangle, and a right triangle to form the figure shown.

Mathematics

1 answer:

pashok25 [27]3 years ago

3 0

I believe the answer is 10

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Three semicircles are placed in a rectangle, as shown below. The width of the 3 rectangle is 15 . Find the area of the shaded re

Leni [432]

Answer:

Step-by-step 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.

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