Area and Volume Unit Test

Question

5 of 155 of 15 Items

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)
Choose a 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
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Answer 1

To find the area of the polygon, we first need to calculate the area of each individual rectangle and then subtract the overlapping areas.

Area of the upper vertical rectangle: 5 * 12 = 60 square units
Area of the lower vertical rectangle: 6 * 12 = 72 square units
Area of the horizontal rectangle: 5 * 3 = 15 square units

Total area = 60 + 72 + 15 = 147 square units

Due to the overlapping areas, we need to subtract them:
Area of overlapping part in the upper vertical rectangle = 5 * 3 = 15 square units
Area of overlapping part in the lower vertical rectangle = 5 * 3 = 15 square units

Total overlapping area = 15 + 15 = 30 square units

Final area = Total area - Total overlapping area
Final area = 147 - 30 = 117 square units

Therefore, the correct answer is:
83 square units