Compute the area of the shape. Show all your work, explain your reasoning when necessary. You cannot assume that any of the unlabeled angles are right angles.

lel12 Nov 18, 2022

#1**0 **

Connect the LEFT angle with the RIGHT angle with a straight line.

Now, you have triangle SAS with 5, angle 72, and 11.

Acute scalene triangle.

Sides: a = 5 b = 11 c = 10.583

**Area: T = 26.154 [use Heron's formula]**

Perimeter: p = 26.583

Semi-perimeter: s = 13.292

At the bottom half of the shape, you have an SSS triangle with sides:7, 8 and 10.583

Solve the SSS triangle:

Acute scalene triangle.

Sides: a = 10.583 b = 7 c = 8

**Area: T = 27.999==28 [use Heron's formula]**

Perimeter: p = 25.583

Semi-perimeter: s = 12.792

Add the above 2 highlighted areas of 26.154 and 27.999

**26.154 + 28 (rounded) ==54.154 units^2 - area of the shape**

Guest Nov 18, 2022