Question

find the area of a trapezoid by decomposing it into other shapes the numbers are 10 on the top 7 on the right side and 13 on the bottom

Answer 1

To find the area of a trapezoid by decomposing it into other shapes, we can split the trapezoid into a rectangle and two right triangles.

First, we need to find the height of the trapezoid. We can do this by drawing a perpendicular line from the top of the trapezoid down to the base. This divides the trapezoid into a rectangle and two right triangles, where the height is the base of the right triangle.

Using the Pythagorean theorem, we find that the height of the trapezoid is 5 units.

Next, we can decompose the trapezoid into a rectangle and two right triangles.

The rectangle has dimensions of 10 units (top base) and 13 units (bottom base). Therefore, the area of the rectangle is 10 * 5 = 50 square units.

Each right triangle has a base of 3 units and a height of 5 units. The area of each right triangle is (1/2) * base * height = (1/2) * 3 * 5 = 7.5 square units.

Since there are two right triangles, the total area of the right triangles is 2 * 7.5 = 15 square units.

Therefore, the total area of the trapezoid is the sum of the area of the rectangle and the area of the right triangles:

Area = 50 + 15 = 65 square units

So, the area of the trapezoid is 65 square units.