Three semicircles are placed in a rectangle as shown below. The length of the rectangle is 48cm . Find the area of the shaded region. Use the value 3.14 for

Question

Three semicircles are placed in a rectangle as shown below. The length of the rectangle is
48cm
.
Find the area of the shaded region. Use the value
3.14
for
π
, and do not round your answer.
Be sure to include the correct unit in your answer.

 

3 semicircles inside a rectangle side by side (ooo) but semicircle inside a rectangle. shaded area is above the semicircles that do not fill in on top. 

Answer 1

Assuming the three circles touch each other in one point and that they touch all four sides of the rectangle, divide the 48 cm by 3 to get that the diameter of each circle is 16 cm. 

 

The area of the whole rectangle is 48 x 16 = 768 cm².

 

The radius of each circle is 16 (diameter) ÷ 2, 8 cm.

 

The area of each circle is π (8)², so 64π. Using 3.14 for π, that is 200.96.  There are 3 circles, so together they are 602.88.

 

The area of the rectangle that is not in a circle is 768-602.88=165.12. 

 

Since they only area they want is the top part, divide the 165.12 by 2, to get 82.56 cm².