The semicircles and the equivalent triangles in the figure are congruent. If the radius of the semicircle is "r", what is the total area of the shape?
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Given : The semicircles and the equilateral triangles in the figure are congruent the radius of the semicircle is "r",
To Find : the total area of the shape
(2√3 π) (r²)
(2√3 + π) (r²)
(√3/4 + π) (r²)
(√3/8 + π) (r²)
Solution:
radius of semi circle = r
area of semicircle = (1/2)πr²
Area of 2 semicircles= 2 * (1/2)πr² = πr²
Diameter = 2 * radius = 2r = Side of triangle
Area of Equilateral triangle = (√3 / 4) ( 2r)²
= √3 r²
Area of 2 Equilateral triangle = 2 * √3 r²
= 2√3 r²
Total Area of the shape = πr² + 2√3 r²
= (2√3 + π) (r²)
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