Question

One elegant hotel has a grand dining room. Each of the room’s three walls facing the gardens contains 8 insulated windows. The dimensions of the window are shown. When the windows were insulated, a glaze was applied to the exterior face to seal each window from weather elements. Which of the following equations could the contractor have used to determine the amount of glaze, g, required?

Answer 1

Option A

`\displaystyle A_t=(3*8)(36*60+(1)/(2)\ \pi *18^2)`

Explanation:

Area of compound figures

When we fid a compound shape, we must try to break it down into two standard shapes, find their areas using formulas and then add them to compute the final area.

The image provided in the question corresponds to a semi-circle on top of a rectangle. All the dimensions are given, so we can compute the area of each part of the window, add them to find the total area of the window, and finally multiply it by the total number of windows that were insulated with a glaze.

The area of a rectangle of dimensions X,Y is

`\displaystyle A_R= X.Y`

Our window has dimensions 36 in by 60 in, so

`\displaystyle A_R=36*60`

The top of the window is half a circle, which area is computed as

`\displaystyle A_(SC)=(\pi\ r^2)/(2)=(\pi*18^2)/(2)=(1)/(2)\ \pi*18^2`

The total of each window is the sum of the above

`\displaystyle A_w=36*60+(1)/(2)\pi*18^2`

The hotel's grand dining room has three walls facing the gardens, each of which contains 8 insulated windows. The total area of the windows is (3*8) times the area of each window

`\boxed{\displaystyle A_t=(3*8)(36*60+(1)/(2)\ \pi *18^2)}`

This result corresponds to the option A