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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.
To find the area of the polygon, we need to find the area of the rectangle and the area of the trapezoid, and then add them together.
Area of rectangle = length x width
Area of rectangle = 7.2 x 6
Area of rectangle = 43.2
Next, we need to find the area of the trapezoid. The formula for the area of a trapezoid is A = 0.5 x (a + b) x h, where a and b are the lengths of the bases and h is the height.
In this case, the bases of the trapezoid are the width of the rectangle (6) and the length of the part that extends outward (1).
Area of trapezoid = 0.5 x (6 + 1) x 3
Area of trapezoid = 0.5 x 7 x 3
Area of trapezoid = 10.5
Now, we can find the total area of the polygon by adding the area of the rectangle and the area of the trapezoid together.
Total area = area of rectangle + area of trapezoid
Total area = 43.2 + 10.5
Total area = 53.7
Therefore, the area of the polygon is 53.7 square units.