# GMAT Math : Calculating the length of the side of a quadrilateral

## Example Questions

### Example Question #32 : Other Quadrilaterals

The area of a trapezoid is 1,600 square centimeters. Its height is 24 centimeters, and one base is one decimeter longer than the other. What is the length of the longer base?

Explanation:

Let  be the longer base. Then, since this is ten centimeters (= 1 decimeter) longer than the shorter, the shorter base has length . Substitute  in the formula for the area of a trapezoid, and solve for :

centimeters

### Example Question #33 : Other Quadrilaterals

The area of a trapezoid is 6,000 square inches. Its height is twice the length of its ionger base, which is three times the length of its shorter base. What is the height of the trapezoid?

Explanation:

Let  be the length of the shorter base. Then  is the length of its longer base, and  is the height. Substitute  in the area formula:

The height is six times this, or  inches.

### Example Question #1 : Calculating The Length Of The Side Of A Quadrilateral

A trapezoid has bases of length one mile and 4,000 feet and height one-half mile. What is the length of its midsegment?

Explanation:

The length of the midsegment of a trapezoid is the mean of the lengths of its bases; the height is irrelevant. The bases are of length 4,000 feet and 5,280 feet; their mean is

feet, the length of the midsegment.

### Example Question #122 : Quadrilaterals

A given trapezoid has an area of , a longer base of length  , and a height of . What is the length of the shorter base?

Explanation:

The area  of a trapezoid with a larger base , a shorter base , and a height  is defined by the equation . Restructuring to solve for the shorter base :

Plugging in our values for , , and

### Example Question #3 : Calculating The Length Of The Side Of A Quadrilateral

A given trapezoid has an area of , a longer base of length  , and a height of . What is the length of the shorter base?

Explanation:

The area  of a trapezoid with a larger base , a shorter base , and a height  is defined by the equation . Restructuring to solve for the shorter base :

Plugging in our values for , and

### Example Question #4 : Calculating The Length Of The Side Of A Quadrilateral

A given trapezoid has an area of , a longer base of length  , and a height of . What is the length of the shorter base?

Explanation:

The area  of a trapezoid with a larger base , a shorter base , and a height  is defined by the equation . Restructuring to solve for the shorter base :

Plugging in our values for , and

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