Trapezoid PQRS has parallel sides PQ and RS with lengths of 7 centimeters and 13 centimete… — GRE General Test

Trapezoid $PQRS$ has parallel sides $PQ$ and $RS$ with lengths of $7$ centimeters and $13$ centimeters, respectively. If the perpendicular height between these parallel sides is $4$ centimeters, what is the area of trapezoid $PQRS$ , in square centimeters?

A
$24$
B
$28$
$40$ Answer
D
$52$
E
$80$

Answer

The area of trapezoid

PQRS

40

square centimeters.

The area of a trapezoid is found by averaging the lengths of the two parallel bases and multiplying by the perpendicular height:

\text{Area} = \frac{7 + 13}{2} \times 4 = 10 \times 4 = 40

square centimeters.

Step-by-Step Solution

Identify the formula for the area of a trapezoid

\text{Area} = \frac{b_1 + b_2}{2} \times h

, where

b_1

and

b_2

are the lengths of the parallel bases and

h

is the height.

The area of any trapezoid is equal to the average of its parallel bases multiplied by its perpendicular height.

Substitute the given dimensions into the formula

\text{Area} = \frac{7 + 13}{2} \times 4

The given bases are

b_1 = 7\text{ cm}

and

b_2 = 13\text{ cm}

, and the height is

h = 4\text{ cm}

Calculate the average base length and multiply by the height

\frac{20}{2} \times 4 = 10 \times 4 = 40\text{ cm}^2

Simplifying

\frac{7 + 13}{2}

gives

10

, and

10 \times 4 = 40

Key Concept

Trapezoid Area Formula

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic