GMAT Math : Quadrilaterals

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Example Questions

Example Question #31 : Quadrilaterals

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?

Possible Answers:

$\dpi{100} \small 48in.$

$\dpi{100} \small 40in.$

$\dpi{100} \small 24in.$

$\dpi{100} \small 36in.$

$\dpi{100} \small 12in.$

Correct answer:

$\dpi{100} \small 48in.$

Explanation:

If the area of the rectangle is equal to the area of the square, then it must have an area of $\dpi{100} \small 144in^{2}$ $\dpi{100} \small (12\times 12)$ . If the rectangle has an area of $\dpi{100} \small 144 in^{2}$ and a side with a lenth of 3 inches, then the equation to solve the problem would be $\dpi{100} \small 144=3x$ , where $\dpi{100} \small x$ is the length of the rectangle. The solution:

$\frac{144}{3} = 48$ .

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Example Question #31 : Rectangles

A rectangle twice as long as it is wide has perimeter 6N - 12 . Write its area in terms of .

Possible Answers:

$2N^{2} -6N + 4$

$4N^{2} -16N + 16$

$2N^{2} -8N + 8$

$N^{2} -4N + 4$

$N^{2} -3N + 2$

Correct answer:

$2N^{2} -8N + 8$

Explanation:

Let be the width of the rectangle; then its length is L = 2W , and its perimeter is

2W + 2 (2W) = 2W + 4W = 6W

Set this equal to 6N - 12 and solve for :

6W = 6N - 12

$\frac{6W}{6} =\frac{ 6N-12}{6}$

W = N - 2

The width is W = N - 2 and the length is $L = 2W = 2 \left (N - 2 \right ) = 2N - 4$ , so multiply these expressions to get the area:

$A = LW = (N-2) \cdot \left (2N-4 \right ) = 2N^{2} -8N + 8$

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Example Question #32 : Rectangles

A rectangle has its vertices at (-4,-3), (-4,7), (1,7), (1,-3) . What part, in percent, of the rectangle is located in Quadrant III?

Possible Answers:

$12\%$

$21 \%$

$14 \%$

$28 \%$

$24 \%$

Correct answer:

$24 \%$

Explanation:

A rectangle with vertices (-4,-3), (-4,7), (1,7), (1,-3) has width 1 - (-4) = 5 and height 7 - (-3) = 10 , thereby having area $10 \times 5 = 50$ .

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

(-4,-3), (-4,0), (0,0), (0,-3) .

It has width 0-(-4) = 4 and height 0-(-3) = 3 , thereby having area $4 \times 3 = 12$ .

Therefore, $\frac{12}{50 }$ of the rectangle is in Quadrant III; this is equal to

$\frac{12}{50 } \times 100 = 24 \%$

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Example Question #3 : Calculating The Area Of A Rectangle

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

Possible Answers:

0.5

Correct answer:

Explanation:

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

A=lw

A=(10)(5)

A=50

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Example Question #5 : Calculating The Area Of A Rectangle

What polynomial represents the area of a rectangle with length A + 4 and width A - 4 ?

Possible Answers:

$A ^{2} -8A + 16$

$A ^{2} - 16$

$A ^{2} + 16$

Correct answer:

$A ^{2} - 16$

Explanation:

The area of a rectangle is the product of the length and the width. The expression (A+4)(A-4) 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

$(A+4)(A-4) = A^{2}-4^{2}= A^{2}-16$

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Example Question #4 : Calculating The Area Of A Rectangle

A rectangle has its vertices at (-4,-3), (-4,7), (1,7), (1,-3) . What percentage of the rectangle is located in Quadrant IV?

Possible Answers:

$3\%$

$4 \%$

$2 \%$

$5\%$

$6 \%$

Correct answer:

$6 \%$

Explanation:

A rectangle with vertices (-4,-3), (-4,7), (1,7), (1,-3) has width 1 - (-4) = 5 and height 7 - (-3) = 10 ; it follows that its area is $10 \times 5 = 50$ .

The portion of the rectangle in Quadrant IV has vertices (0,0),(1,0), (1, -3), (0, -3) . Its width is 1-0 = 1 , and its height is 0- (-3 ) = 3 , so its area is $1 \times 3 = 3$ .

Therefore, $\frac{3}{50 }$ , or $\frac{3}{50} \times 100 \% = 6\%$ , of this rectangle is in Quadrant IV.

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Example Question #6 : Calculating The Area Of A Rectangle

The perimeter of a rectangle is $104\textup{ inches}$ and its length is times the width. What is the area?

Possible Answers:

$52\textup{ in}^2$

$208\textup{in}^{3}$

$10816\textup{ in}^2$

$208\textup{ in}^2$

$507\textup{ in}^2$

Correct answer:

$507\textup{ in}^2$

Explanation:

The perimeter of a rectangle is the sum of all four sides, that is: 104= 2l + 2w

since l=3w , we can rewrite the equation as:

104= 2(3w) + 2w

104= 8w

$w=13\textup{ in}$

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.

$l=3w=3(13)=39\textup{ in}$

$A= l \cdot w = 39 \cdot 13$

$A = 507\textup{ in}^2$

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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?

Possible Answers:

300ft^2

25ft^2

250ft^2

30ft^2

Correct answer:

250ft^2

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 3(10)

So put it together:

3(10)-5=30-5=25ft

Next, find the area via the following formula:

A=l*w=25ft*10ft=250ft^2

So our answer is:

250ft^2

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Example Question #5 : Calculating The Area Of A Rectangle

Find the area of a rectangle whose side lengths are $7\textup{ and }9$ .

Possible Answers:

Correct answer:

Explanation:

To calculate area, multiply width times height. Thus,

7*9=63

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Example Question #6 : Calculating The Area Of A Rectangle

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

Possible Answers:

2x+2y

4x+4y

4xy

2xy

Correct answer:

4xy

Explanation:

To find area, simply multiply length times width. Thus

$2x\cdot2y=4xy$

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GMAT Math : Quadrilaterals

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #31 : Quadrilaterals

Example Question #31 : Rectangles

Example Question #32 : Rectangles

Example Question #3 : Calculating The Area Of A Rectangle

Example Question #5 : Calculating The Area Of A Rectangle

Example Question #4 : Calculating The Area Of A Rectangle

Example Question #6 : Calculating The Area Of A Rectangle

Example Question #8 : Calculating The Area Of A Rectangle

Example Question #5 : Calculating The Area Of A Rectangle

Example Question #6 : Calculating The Area Of A Rectangle

All GMAT Math Resources

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