A municipal park features a garden in the shape of a trapezoid. The parallel sides of the … — Armed Services Vocational Aptitude Battery (ASVAB)

A municipal park features a garden in the shape of a trapezoid. The parallel sides of the garden measure $18$ meters and $12$ meters. If the total area of the garden is $150$ square meters, what is the perpendicular distance between the parallel sides?

A
$5$ meters
$10$ metersAnswer
C
$30$ meters
D
$50$ meters

Answer

The perpendicular distance between the parallel sides is

10

meters.

The correct answer accurately applies the trapezoid area formula. By setting

150 = \frac{1}{2}(18 + 12)h

, the sum of the bases is calculated as

30

. Multiplying by

\frac{1}{2}

results in

15

. Dividing the total area (

150

) by

15

yields a perpendicular height of

10

meters.

Step-by-Step Solution

Identify the formula for the area of a trapezoid.

A = \frac{1}{2}(b_1 + b_2)h

This formula relates the known area and bases to the unknown height.

Substitute the known values into the formula.

150 = \frac{1}{2}(18 + 12)h

The given area is

150

, and the bases are

18

and

12

Simplify the sum inside the parentheses.

150 = \frac{1}{2}(30)h

Adding the lengths of the bases gives

30

Multiply

30

\frac{1}{2}

150 = 15h

This isolates the variable term

h

Divide both sides by

15

to solve for

h

h = 10

Dividing by

15

determines the perpendicular height.

Key Concept

Using the area formula of a trapezoid to solve for an unknown dimension.

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