Area of Composite Figures Quick Check
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Question
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
To find the area of the figure, we need to first find the area of the outer polygon and then subtract the area of the smaller rectangular piece that is missing.
The outer polygon can be divided into a rectangle with dimensions 6 by 8 and a triangle with base 6 and height 2.
Area of rectangle = 6 * 8 = 48 square units
Area of triangle = (1/2) * 6 * 2 = 6 square units
Total area of the outer polygon = 48 + 6 = 54 square units
Now, we subtract the area of the missing rectangle which has dimensions 2 by 6.
Area of missing rectangle = 2 * 6 = 12 square units
Final area of the figure = 54 - 12 = 42 square units
Therefore, the correct answer is not listed among the options provided.