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

77 square units
77 square units

83 square units
83 square units

68 square units
68 square units
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of the polygon, we need to break it down into smaller shapes. The polygon is made up of two rectangles (with dimensions 12 x 3 and 5 x 3) and two triangles.

Area of the first rectangle = 12 x 3 = 36 square units
Area of the second rectangle = 5 x 3 = 15 square units

To find the area of the triangles, we need to find their base and height. The base of each triangle is 3 units (the width of the vertical sides) and the height is h units.

Using the Pythagorean Theorem, we can find the height:
h^2 + 3^2 = 6^2
h^2 + 9 = 36
h^2 = 27
h ≈ 5.2 (rounded to 1 decimal place)

Now we can find the area of each triangle:
Area of first triangle = (1/2) x 3 x 5.2 ≈ 7.8 square units
Area of second triangle = (1/2) x 3 x 5.2 ≈ 7.8 square units

Finally, we can add up the areas of all the shapes to find the total area of the polygon:
36 + 15 + 7.8 + 7.8 = 66.6 square units

Therefore, the closest answer among the options provided is 68 square units.