Question

Find the area of the following shape. You must show all work to receive credit.

Answer 1

Answer:

51.5 square units

Step-by-step explanation:

To find the area of an irregular shape, one method that can be used is to divide the area into simple shapes. Then you calculate the area of each simple shape using a known formula. Finally, you add all the areas together.

Let's divide the area into 2 trapezoids and 1 triangle.

First trapezoid at the bottom:

Draw a segment from point F to (11, -6), which is 2 units above B.

Below this segment, there is a trapezoid with base lengths: 11 and 6, and height 2.

Area of first trapezoid = (b1 + b2)h/2 = (11 + 6)(2)/2 = 17

Second trapezoid in the middle:

Draw a segment from point E through point D and ending at point (11, -3).

Below this segment, there is a trapezoid with base lengths: 11 and 7, and height 3.

Area of second trapezoid = (b1 + b2)h/2 = (11 + 7)(3)/2 = 27

Triangle on top:

The segment from point D to point (11, -3) is the bottom side of a triangle whose base is 5 and whose height is 3.

Area of triangle = bh/2 = (5)(3)/2 = 7.5

Total Area = Area of first trapezoid + area of second trapezoid + area of triangle

Total Area = 17 + 27 + 7.5

Total Area = 51.5