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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?
To find the area of the figure, we first need to calculate the area of the entire polygon and then subtract the area of the missing rectangle.
First, calculate the area of the entire polygon. Since the top and bottom sides are parallel, we can treat it as a trapezoid.
Area of a trapezoid = ((a + b) / 2) * h
= ((6 + 6) / 2) * 8
= (12 / 2) * 8
= 6 * 8
= 48
Next, calculate the area of the missing rectangle.
Since the top and bottom sides are each 6 units long and the width of the missing piece is 2, the remaining height of the trapezoid is 6 - 2 = 4 units.
Area of the missing rectangle = 2 * 4
= 8
Now, subtract the area of the missing rectangle from the area of the entire polygon to find the area of the figure.
Area of the figure = 48 - 8
= 40
Therefore, the area of the figure is 40 square units.