Question

THE SEMICIRCLES AND THE EQUIVALENTI
TRIANGLES IN THE FIGURE ARE CONGRUE
IF THE RADIUS OF THE SEMICIRCLE IS '
WHAT IS THE TOTAL AREA OF THE SHAPE?​

Answer 1

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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