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ISEE Upper Level Math : How to find the perimeter of a trapezoid

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Example Questions

Example Question #261 : Plane Geometry

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 $10 \ in$ $\displaystyle 10 \ in$. If the perimeter of the trapezoid is $56\ in$ $\displaystyle 56\ in$, give the length of the smaller base.

Possible Answers:

$12\ in$ $\displaystyle 12\ in$

$10\ in$ $\displaystyle 10\ in$

$15\ in$ $\displaystyle 15\ in$

$16\ in$ $\displaystyle 16\ in$

$14\ in$ $\displaystyle 14\ in$

Correct answer:

$12\ in$ $\displaystyle 12\ in$

Explanation:

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

$\displaystyle Perimeter=a+b+c+d$,

where a+b+c+d $\displaystyle a+b+c+d$ are the lengths of each side.

Let $\displaystyle b=$ small base length and 2b= $\displaystyle 2b=$ big base length.

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

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Example Question #261 : Geometry

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

The following is given:

a=2x $\displaystyle a=2x$

b=3x $\displaystyle b=3x$

c=1.5x $\displaystyle c=1.5x$

d=1.7x $\displaystyle d=1.7x$

Find $\displaystyle x$.

Figure not drawn to scale.

Trapezoidr

Possible Answers:

$\displaystyle 5$

$\displaystyle 4$

$\displaystyle 10$

$\displaystyle 1$

$\displaystyle 3$

Correct answer:

$\displaystyle 5$

Explanation:

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

$\displaystyle Perimeter=a+b+c+d$,

where a,b,c,d $\displaystyle a,b,c,d$ are the lengths of each side.

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

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ISEE Upper Level Math : How to find the perimeter of a trapezoid

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #261 : Plane Geometry

Example Question #261 : Geometry

All ISEE Upper Level Math Resources

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