Use the image to answer the question.
An illustration shows a polygon where the top, right, and bottom sides are perpendicular to each other. A smaller rectangular piece is missing from the center of the left side of the polygon inward. The dimensions are as follows: the top side is 6, the right side is 8, and the bottom side is 6. The left side is divided into three parts. It shows a vertical width of 2 from the top
Solve the following problem using what you know about composite figures. What is the area of the figure?
(1 point)
Responses
30 square units
30 square units
48 square units
48 square units
36 square units
36 square units
24 square units
24 square units
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To find the area of the figure, we first need to find the area of the full polygon and then subtract the area of the missing rectangle.
The area of the full polygon can be calculated by finding the area of the two right triangles formed by the perpendicular sides and the rectangle in the center.
Area of the first right triangle = (base * height) / 2 = (6 * 2) / 2 = 6 square units
Area of the second right triangle = (base * height) / 2 = (6 * 4) / 2 = 12 square units
Area of the rectangle = length * width = 2 * 4 = 8 square units
Total area of the full polygon = 6 + 12 + 8 = 26 square units
Therefore, the area of the missing rectangle = 26 - 24 = 2 square units
Answer: 24 square units