Question

Calculate the area of rectangle

Answer 1

Given :  Rectangle , arc and semicircle and tangent to semicircle from one vertex of rectangle

To find : Area of rectangle

Solution:

Let say R is Radius  of arc in rectangle

& r is the radius of  the semicircle

Then sides of rectangle would  be  R   & ( R + r + r)

=> R & (R + 2r)

Area of rectangle   = R(R + 2r)

= R² + 2Rr

5 cm is the Tangent to the Semicircle

Distance of point from center = R + r

radius of semicircle = r

=> ( R + r)²  = 5² + r²

=> R² + r² + 2Rr = 25 + r²

=> R² + 2Rr = 25

Area of rectangle   =  R² + 2Rr = 25  cm²

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