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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. 

 Nov 18, 2022
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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

 Nov 18, 2022

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