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A polygon is shaped like a trapezoid attached to the top of a vertical rectangle. The length of the rectangle is 7.2 and the width is 6. The perpendicular height of the trapezoid is 3, marked with a dashed vertical line forming an extension of the rectangle to the top left vertex of the trapezoid. The part of trapezoid that extends outward and perpendicular to both sides of the rectangle measures 1.
Find the area of the polygon.
(1 point)
square units
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To find the area of the polygon, we first need to find the areas of the rectangle and trapezoid separately, then add them together.
The area of the rectangle is length times width, so:
Area of rectangle = 7.2 * 6 = 43.2 square units
Next, we need to find the area of the trapezoid. The formula for the area of a trapezoid is: ((a + b) * h) / 2, where a and b are the lengths of the two parallel sides and h is the perpendicular height.
In this case, the parallel sides are 6 and 1, and the height is 3, so:
Area of trapezoid = ((6 + 1) * 3) / 2 = (7 * 3) / 2 = 21 / 2 = 10.5 square units
Finally, we can find the total area of the polygon by adding the areas of the rectangle and trapezoid together:
Total area = 43.2 + 10.5 = 53.7 square units
Therefore, the area of the polygon is 53.7 square units.