Question

Fine the area of the polygon in square units. Shaped like an L. Top of L is 7. Inside of L is 13. Bottom at the angle is 15 and the right end of the L is also 7

Answer 1

To find the area of the polygon shaped like an L, we need to divide it into two separate shapes - a rectangle and a right triangle.

First, let's find the area of the rectangle. The width of the rectangle is 7 units and the length is 13 units.
Area of rectangle = length x width
Area of rectangle = 13 x 7
Area of rectangle = 91 square units

Next, let's find the area of the right triangle. The base of the triangle is 7 units and the height can be found using the Pythagorean theorem.
a^2 + b^2 = c^2
Given that the base is 7 and the hypotenuse is 15:
7^2 + b^2 = 15^2
49 + b^2 = 225
b^2 = 176
b = √176
b ≈ 13.27

Area of triangle = (base x height) / 2
Area of triangle = (7 x 13.27) / 2
Area of triangle ≈ 46.47 square units

Therefore, the total area of the polygon shaped like an L is:
91 (rectangle) + 46.47 (triangle) ≈ 137.47 square units