How to find the perimeter of a trapezoid

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ISEE Upper Level Quantitative Reasoning › How to find the perimeter of a trapezoid

Questions 1 - 2

1

The bigger base length of a trapezoid is two times bigger than the smaller base length. Legs of the trapezoid have the same length of $10 \ in$ . If the perimeter of the trapezoid is $56\ in$ , give the length of the smaller base.

$12\ in$

$14\ in$

$15\ in$

$16\ in$

$10\ in$

Explanation

Like any polygon, the perimeter of a trapezoid is the total distance around the outside, i.e.

,

where are the lengths of each side.

Let small base length and big base length.

$b+2b+10+10=56\Rightarrow 3b=36\Rightarrow b=12\ in$

2

The perimeter of the following trapezoid is $41\ cm$ .

The following is given:

Find .

Figure not drawn to scale.

Trapezoidr

Explanation

The perimeter of a trapezoid is equal to the sum of all of the sides, i.e.

,

where are the lengths of each side.

$2x+3x+1.5x+1.7x=41\Rightarrow 8.2x=41\Rightarrow x=41\div 8.2=5$

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