Question

The Norman window illustrated below has a semicircular section on top of a rectangle. The radius of the semicircle is x. The long side of the rectangle is three times the radius of the semicircle.

a)Express the total area of the window, A, as a function of x.
b) Express the outer perimeter of the window, P, as a function of x.

Answer 1

area of window=x*3x+PI*x^2
Perimeter=2*3x+x+PI*r

This is hardly calculus.

Answer 2

The rectangle is 2x by 3x with the semicircle on top of the 2x side
Since there is a semicircle on top of the rectangle, the area

= rectangle + semicircle
= basexheight + (1/2)π x^2
= (2x)(3x) + π x^2/2
= 6x^2 + πx^2/2

perimeter = (1/2)(2πx) + 2x + 2(3x)
= πx + 8x