A window is in the shape of a square with a side of length s, with a semicircle of diameter s, adjoining the top of the square.

Question

Write the total area of the window W as a function of s
Hint. Start with a formula for the area of a square and the area of a circle. 

Answer 1

Total Area = Area of the square plus area of the semi-circle

A = s^2 + (1/2)pi(s/2)^2 = s^2 +pi(s^2)/8 = s^2(1+pi/8)

A=s^2(1+pi/8)

the area of the semi-circle = one half the area of a circle with radius s/2

area of a circle = pi(r)^2= pi(s/2)^2 = pi(s^2)/4

half the circle's area = (1/2)pi(s^2)/4 = pi(s^2)/8