Question

The window shown here is a composite of a rectangle and a semicircle. If each square of the grid is six inches by six inches, what is the perimeter of the rectangular part of the window, ABCD? Include only the outside perimeter.

Answer 1

So break it up into 2 parts.

The bottom rectangle:
The length from A to D is 8 blocks, which is the same as the length from BC.
The length of D to C is 6 blocks.

So the length from A to D to C to B is 8 blocks + 6 blocks + 8 blocks = 22 blocks

The top circle:
Find the circumference of the circle using C = pi * diameter
The diameter is 6 blocks, so the circumference is:
C = pi * 6
you only have half of the circle so you must divide that by 2, so its:
pi * 6 / 2 = pi * 3

Add those 2 parts together and your total perimeter is:
22 blocks + pi * 3 blocks

calculate that then multiply that by 6, since each block is 6 inches

Answer 2

132 inches

Explanation:

We need to find the perimeter of the rectangular part of the window, ABCD include only the outside perimeter. It means that we need to know the length of sides AD, DC and BC only and then the perimeter is the sum of those 3 sides.

Given that:

A square of the grid is six inches by six inches

• From point A to point D or point B to C, there are 8 square in vertical.

=> AD or BC = 8 * 6 inches = 48 inches long

From point D to point C, there are 6 square in horizontal

=> DC = 6 * 6 inches = 36 inches long

=> the perimeter of the rectangular part of the window, ABCD which include only the outside perimeter is:

AD+ DC +BC = 48 + 36 + 48 = 132 inches