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# Geometry

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The trapezoid shown has a height of length 12 cm, a base of length 16 cm, and an area of 180 cm^2. What is the perimeter of the trapezoid?

Nov 5, 2021

#1
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What is the perimeter of the trapezoid?

Helo Guest!

$$A=\frac{h(a+b)}{2}\\ b= \frac{2A}{h}-a=\frac{2\cdot 180cm^2}{12cm}-16cm$$

$$b=14cm$$

$$P=a+b+h+\sqrt{h^2+(a-b)^2}=(14+16+12+\sqrt{12^2+(16-14)^2})cm$$

$$P=54.17cm$$

!

Nov 5, 2021
edited by asinus  Nov 5, 2021