# The semicircle of area 50 pi centimeters is inscribed inside a rectangle. The diameter of the semicircle coincides with the length of the rectangle. Find the area of the rectangle.

1
by ajhing16
The semicircle of area 50 pi centimeters is inscribed inside a rectangle. The diameter of the semicircle coincides with the length of the rectangle. Find the area of the rectangle.

2015-01-11T15:06:24+08:00
Area of a circle =
Area of a rectangle = base x height

Semicircle:
A =
2(50 )= r²      --> i multiplied 50  by 2 since 50

The area of the rectangle is 200 cm².

For the radius is 10 cm. :)
What the? huhu~ my solutions not yet finished. :'( why can't I re-edit it again?
Area of a circle = $$\pi$$r²
Area of a rectangle = length x width

Semicircle:
A = $$\pi$$r²
2(50 $$\pi$$)= $$\pi$$r² --> I multiplied 50 $$\pi$$ by 2 since 50 $$\pi$$ is the area of the semicircle.
Area of a circle = pi r²
Area of a rectangle = length x width

Semicircle:
A = pi r²
2(50 pi ) = pi r² --> I multiplied 50 pi by 2 since 50 pi is the area of the semicircle

(100 pi = pi r²) pi
r² = 100
r = 10 cm

Rectangle: (A = length x width)

length = diameter of the semicircle
= 2(10 cm)
= 20 cm
width = radius of the semicircle
= 10 cm

so, A = l x w
= 20 (10)
= 200 cm
*facepalm* sorry for the unwanted comments... jeez... anyways, the above comment is the REAL solution...
*facepalm* for the 987654321 times, i committed a mistake again.... jeez, I am very sorry. In the comment where I put the real solution - it's answer is 200 cm². not 200 cm... :)