# GMAT Math : Calculating the area of a rectangle

## Example Questions

### Example Question #1 : Calculating The Area Of A Rectangle

The area of a square that has sides with a length of 12 inches is equal to the area of a rectangle. If the rectangle has a width of 3 inches, what is the length of the rectangle?

Explanation:

If the area of the rectangle is equal to the area of the square, then it must have an area of  . If the rectangle has an area of  and a side with a lenth of 3 inches, then the equation to solve the problem would be , where  is the length of the rectangle. The solution:

.

### Example Question #2 : Calculating The Area Of A Rectangle

A rectangle twice as long as it is wide has perimeter . Write its area in terms of .

Explanation:

Let  be the width of the rectangle; then its length is , and its perimeter is

Set this equal to  and solve for :

The width is  and the length is  ,  so multiply these expressions to get the area:

### Example Question #3 : Calculating The Area Of A Rectangle

A rectangle has its vertices at . What part, in percent, of the rectangle is located in Quadrant III?

Explanation:

A rectangle with vertices  has width  and height  , thereby having area .

The portion of the rectangle in Quadrant III is a rectangle with vertices

.

It has width  and height , thereby having area  .

Therefore,  of the rectangle is in Quadrant III; this is equal to

### Example Question #1 : Calculating The Area Of A Rectangle

What is the area of a rectangle given the length of  and width of ?

Explanation:

To find the area of a rectangle, you must use the following formula:

### Example Question #5 : Calculating The Area Of A Rectangle

What polynomial represents the area of a rectangle with length  and width  ?

Explanation:

The area of a rectangle is the product of the length and the width. The expression  can be multplied by noting that this is the product of the sum and the difference of the same two terms; its product is the difference of the squares of the terms, or

### Example Question #31 : Quadrilaterals

A rectangle has its vertices at . What percentage of the rectangle is located in Quadrant IV?

Explanation:

A rectangle with vertices  has width  and height  ; it follows that its area is

The portion of the rectangle in Quadrant IV has vertices . Its width is , and its height is , so its area is .

Therefore, , or  , of this rectangle is in Quadrant IV.

### Example Question #7 : Calculating The Area Of A Rectangle

The perimeter of a rectangle is  and its length is  times the width. What is the area?

Explanation:

The perimeter of a rectangle is the sum of all four sides, that is:

since , we can rewrite the equation as:

We are being asked for the area so we still aren't done. The area of a rectangle is the product of the width and length. We know what the width is so we can find the length and then take their product.

### Example Question #8 : Calculating The Area Of A Rectangle

Mark is building a garden with raised beds. One side of the garden will be 10 feet long and the other will be 5 less than three times the first side. What area of will Mark's garden be?

Explanation:

Mark is building a garden with raised beds. One side of the garden will be 10 feet long and the other will be 5 less than three times the first side. What area of will Mark's garden be?

This problem asks us to find the area of a rectangle. We are given one side and asked to find the other. To find the other, we need to use the provided clues.

"...five less..."

"...three times the first side..."  or

So put it together:

Next, find the area via the following formula:

### Example Question #1 : Calculating The Area Of A Rectangle

Find the area of a rectangle whose side lengths are .

Explanation:

To calculate area, multiply width times height. Thus,

### Example Question #381 : Problem Solving Questions

Find the area of a rectangle whose width is  and length is .