Find the area in square inches of this trapezoid-shaped tabletop by decomposing in into simpler shapes. (1 point)
To find the area of the trapezoid-shaped tabletop, we can decompose it into a rectangle and two right triangles.
Let's label the trapezoid as follows:
- Top base: 10 inches
- Bottom base: 14 inches
- Height: 8 inches
We can see that the trapezoid can be decomposed into a rectangle with dimensions 14 inches by 8 inches and two right triangles.
The area of the rectangle is:
Area_rect = length x width
Area_rect = 14 inches x 8 inches
Area_rect = 112 square inches
Each right triangle has a base of 10 - 8 = 2 inches and a height of 8 inches. Therefore, the area of each right triangle is:
Area_triangle = 1/2 x base x height
Area_triangle = 1/2 x 2 inches x 8 inches
Area_triangle = 8 square inches
Since there are two right triangles, the total area contributed by the triangles is:
Total area_triangles = 2 x Area_triangle
Total area_triangles = 2 x 8 square inches
Total area_triangles = 16 square inches
Therefore, the total area of the trapezoid-shaped tabletop is the sum of the area of the rectangle and the total area contributed by the triangles:
Total area = Area_rect + Total area_triangles
Total area = 112 square inches + 16 square inches
Total area = 128 square inches
So, the area of the trapezoid-shaped tabletop is 128 square inches.