Use the image to answer the question.
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 trapezoid separately and then add them together.
1. Area of the rectangle:
Area = length x width
Area = 7.2 x 6
Area = 43.2 square units
2. Area of the trapezoid:
First, we need to find the bases of the trapezoid. One base is the width of the rectangle, which is 6. The other base can be found using the Pythagorean theorem:
a^2 + b^2 = c^2
(6/2)^2 + 1^2 = b^2
3^2 + 1^2 = b^2
9 + 1 = b^2
10 = b^2
b = √10 ≈ 3.16
Now, we can calculate the area of the trapezoid using the formula:
Area = (1/2) x (base1 + base2) x height
Area = (1/2) x (6 + 3.16) x 3
Area = (1/2) x 9.16 x 3
Area = 13.74 square units
3. Total area of the polygon:
Total Area = Area of rectangle + Area of trapezoid
Total Area = 43.2 + 13.74
Total Area = 56.94 square units
Therefore, the area of the polygon is 56.94 square units.