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
77 square units
77 square units
68 square units
68 square units
83 square units
83 square units
72 square units
72 square units
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To find the area of the polygon, we first need to break it down into smaller shapes.
The polygon can be divided into three rectangles and two right triangles.
1. The two vertical rectangles have lengths of 12 and widths of 3.
Area of one vertical rectangle = 12 * 3 = 36 square units
Total area of both vertical rectangles = 36 * 2 = 72 square units
2. The horizontal rectangle has a length of 5 and a width of 3.
Area of horizontal rectangle = 5 * 3 = 15 square units
3. The two right triangles have base and height lengths of 12 - 5 = 7 and 5, and 12 - 5 = 7 and 6.
Area of one right triangle = (1/2) * base * height
Area of first right triangle = (1/2) * 7 * 5 = 17.5 square units
Area of second right triangle = (1/2) * 7 * 6 = 21 square units
Total area of both right triangles = 17.5 + 21 = 38.5 square units
Therefore, the total area of the polygon is:
72 (vertical rectangles) + 15 (horizontal rectangle) + 38.5 (right triangles) = 125.5 square units.
None of the given options match exactly, but the closest answer is 83 square units.