The shape of a garden is square in the middle and two semicircles at the end. If the perimeter of the garden is 72m, find it's area.
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Answers
Let,
Side of square be x metres.
Radius of the semicircles be r metres.
As the diameter is equal to the side of the square,
x = 2r
Perimeter of the garden = 2×(2πr/2) + 2x
= 2πr +2(2r)
= 2πr + 4r
= 2r(π+2) metres
72 = 2r(π+2)
36 = r(π+2)
36 = r[(22/7) + 2]
36 = r(36/7)
r = 7
Now, r = 7m
Therefore, x = 2r = 14m
Now,
Area of the garden = Area of square + 2× Area of semicircle
= x^2 + 2(πr^2/2)
= x^2 + πr^2
= 14^2 + (22/7)×7^2
= 196 + 154
= 350 sq. metres
Therefore, the area of the garden is 350 sq. metres.
Answer:
350 sq. meters
Step-by-step explanation:
Let,
Side of square be x metres.
Radius of the semicircles be r metres.
As the diameter is equal to the side of the square,
x = 2r
Perimeter of the garden = 2×(2πr/2) + 2x
= 2πr +2(2r)
= 2πr + 4r
= 2r(π+2) metres
72 = 2r(π+2)
36 = r(π+2)
36 = r[(22/7) + 2]
36 = r(36/7)
r = 7
Now, r = 7m
Therefore, x = 2r = 14m
Now,
Area of the garden = Area of square + 2× Area of semicircle
= x^2 + 2(πr^2/2)
= x^2 + πr^2
= 14^2 + (22/7)×7^2
= 196 + 154
= 350 sq. metres
Therefore, the area of the garden is 350 sq. metres.
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