What is height h?

Question

Problem 1. The Norman window with dimensions as shown is a rectangle topped by a semicircle. If the area of the window is 44.2 square feet, find its height h. (Round your answer to the nearest whole number.)

*The width is 6 height.

Answer 1

The height and width dimension are switched apparently. Heigh should be 6h and the width should be h. Otherwise the height of the rectangular base alone would be -2! That is impossible.

The diagram of the window would have helped.

Be Well!

Answer 2

Area of your window is area of the rectangle plus the area of the half-circle.

Since you know the width = 6 feet, that means the area of the half-circle is 1/2 times pi times radius squared.

This comes to 4.5*pi.

Area of the rectangle is the width times the height. Height of rectangle is height of window (your variable, h) minus the radius of the half-circle.

Total area is 44.2 ft^2 = 4.5*pi + 6ft*(h-3ft)

Solve this for h, and round as they require.