How to find the length of the side of a trapezoid - ACT Math

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Question

Given the height of a trapezoid is and a base length is , what is the length of the other base if the area of the trapezoid is ?

Answer

Write the formula used to find the area of a trapezoid.

$A=\frac{1}{2}h(b1+b2)$

Substitute the given information to the formula and solve for the unknown base.

$10=\frac{1}{2}(1)(1+b2)$

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Question

is an isosceles trapezoid that is bisected by $\overline{EF}$ .

$\overline{AB} \left | \right | \overline{EF} \left | \right | \overline{DC}$ . If $\overline{AE} = 4$ , $\overline{ED} = 6$ , and $\overline{DC} = 18$ , then what is the length of $\overline{EF}$ ?

Answer

We know that all three horizontal lines are parallel to one another. By definition, we can set up a ratio between the lengths of the sides provided to us in the question and the lengths of the two parallel lines:

$\frac{AE}{ED} = \frac{EF}{DC}$

Once we substitute the given information, we get

$\frac{4}{6}=\frac{EF}{18}$

We cross multiply to solve for EF

$EF = \frac{(4)(18)}{6}$

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