Question

Use the image to answer the question.

An illustration shows the outline of letter upper H. The two vertical sides of the outline letter upper H have length 12 and width 3. The horizontal part across the middle has length 5. The inner side of the upper vertical part of the H has length 5. The inner side of the lower vertical part has length 6.

What is the area of the polygon?

(1 point)
Responses

72 square units
72 square units

68 square units
68 square units

83 square units
83 square units

77 square units
77 square units

Answer 1

The area of the polygon is 72 square units.

To find the area, we need to calculate the area of each individual rectangle formed by the outline of the letter H and then subtract the overlapping area.

Area of the upper vertical rectangle = 12 * 3 = 36 square units
Area of the lower vertical rectangle = 12 * 3 = 36 square units
Area of the horizontal rectangle = 5 * 3 = 15 square units

Total area without overlap = 36 + 36 + 15 = 87 square units

Now we need to subtract the overlap area to get the final answer:

Overlap area = (5-3) * 12 = 24 square units

Final area = Total area without overlap - Overlap area
Final area = 87 - 24
Final area = 63 square units.

Therefore, the area of the polygon is 72 square units.