Question
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 can first find the area of the rectangle and the area of the trapezoid separately, then add them together.
The area of the rectangle is simply the length times the width: 7.2 * 6 = 43.2 square units.
The trapezoid can be split into a smaller rectangle with the same height as the original rectangle and two congruent right triangles on either side. The width of the smaller rectangle is the same as the width of the original rectangle, 6, and the height is the same as that of the trapezoid, 3. Thus, the area of the smaller rectangle is 6 * 3 = 18 square units.
The right triangles each have a height of 3 (the same as the trapezoid) and a base of 1 (the part of the trapezoid that extends outward). The area of one triangle is 0.5 * base * height = 0.5 * 1 * 3 = 1.5 square units. Since there are two such triangles, their total area is 2 * 1.5 = 3 square units.
Now, add the area of the rectangle, the smaller rectangle, and the two triangles together: 43.2 + 18 + 3 = 64.2 square units. So, the area of the polygon is 64.2 square units.