Chapter A.2, Problem 49AYU

To determine

To find: Find the area of the Norman window shown in the illustration. How much wood frame is needed to enclose the window?

Answer to Problem 49AYU

$24+2\pi =30.28 {\text{ft}}^2$; $16+2\pi \text{ft }=22.28\text{ ft}$

Explanation of Solution

Given:

Architecture A Norman window consists of a rectangle surmounted by a semicircle.

Formula Used:

Area of the rectangle $=lw$ and Area of the circle $=\pi r^2$.

Calculation:

Here $l=4, w=6, d=4, r=2$.

Area of the rectangle $=lw=4\times 6=24 {\text{ft}}^2$.

Area of the circle $=\pi r^2=\pi 2^2=4\pi {\text{ft}}^2$.

Area of the semi-circle $=\frac{4\pi }{2}=2\pi {\text{ft}}^2$.

The area of the Norman window $=24+2\pi =30.28 {\text{ft}}^2$.

Circumference of the open rectangle is $l+2w=4+2\times 6=16 \text{ft}$.

Circumference of the semi-circle $=\pi r=\pi \times 2=2\pi \text{ft}$.

The wood frame is needed to enclose the window$=16+2\pi \text{ft }=22.28\text{ ft}$.