The fountain is made up of two semicircles and a quarter circle. find the perimeter and the area of the fountain. round the perimeter to the nearest tenth of a foot and the area to the nearest square foot. both have the diameter 20

The perimeter of the fountain = 94.2 ft

The area of the fountain = 628 ft²

Area of a CircleThe formula of the area of a full circle is: πr².Area of semicircle = ½(πr²)Area of quarter circle = ¼(πr²)Perimeter of a CirclePerimeter of a full circle = 2πrPerimeter of semicircle = ½(2πr)Perimeter of quarter circle = ¼(2πr)

Given:

Diameter of the semicircle = 20 ft

Therefore, Radius (r) = half of diameter = 10 ft

Radius of the quarter circle = 20 ft

Perimeter of the fountain = ½(2πr) + ½(2πr) + ¼(2πr)

Plug in the values of r

Perimeter of the fountain = ½(2π(10)) + ½(2π(10)) + ¼(2π(20))

Perimeter of the fountain = 94.2 ft

Area of the fountain = 2(½(πr²)) + ¼(πr²)

Plug in the values of r

Area of the fountain = 2(½(π10²)) + ¼(π20²)

Area of the fountain = 628 ft²

Learn more about area of a circle on:

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The complete question in the attached figure

we know that
[area of a circle]=pi*r²
[length of the circumference]=2*pi*r

Part A) 
(2 half circles=1 whoole circle)
radius r=20/2----> r=10 ft
[area 2 half circles]=pi*r²----> pi*10²----> 314.16 ft²

[perimeter 2 half circles]=2*pi*r-----> 2*pi*10----> 62.83 ft

Part B)  1/4 big circle
diameter=40 ft
radius=20 ft
[area 1/4 big circle]=pi*r²/4-----> pi*20²/4---> 314.16 ft²
[perimeter of 1/4 big circle]=2*pi*r/4-----> pi*20/2----> 31.42 ft

[area of the fountain]=314.16+314.16-----> 628.32 ft²------> 628 ft²
[perimeter  of the fountain]=62.83+31.42-----> 94.25 ft  -------> 94.3 ft

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