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SSAT Upper Level Math : Perimeter of Polygons

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Example Questions

Example Question #802 : Geometry

The length of a rectangle is 2x+4 and the width of this rectangle is meters shorter than its length. Give its perimeter in terms of .

Possible Answers:

8x+10

10x+8

10x+6

8x+8

8x+6

Correct answer:

8x+10

Explanation:

The length of the rectangle is known, so we can find the width in terms of :

Width=Length-3=(2x+4)-3=2x+1

The perimeter of a rectangle is P=2L+2W , where is the length and is the width of the rectangle.

In order to find the perimeter we can substitute the L=2x+4 and W=2x+1 in the perimeter formula:

P=2L+2W

=2(2x+4)+2(2x+1)

=4x+8+4x+2

=8x+10

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Example Question #803 : Geometry

A rectangle has a length of t^2 inches and a width of inches. Which of the following is true about the rectangle perimeter if t=5 ?

Possible Answers:

Its perimeter is between 8 and 9 feet.

Its perimeter is between 7 and 8 feet.

Its perimeter is more than 8 feet.

Its perimeter is between 7.2 and 7.4 feet.

Its perimeter is less than 7 feet.

Correct answer:

Its perimeter is between 7 and 8 feet.

Explanation:

Substitute t=5 to get and :

L=t^2=5^2=25

$W=5t=5\times 4=20$

The perimeter of a rectangle is P=2L+2W , where is the length and is the width of the rectangle. So we have:

$P=2L+2W=2\times 25+2\times20=50+40=90$ inches

Now we should divide the perimeter by 12 in order to convert to feet:

$Perimeter=90\div 12=7.5$ feet

So the perimeter is 7 feet and 6 inches, which is between 7 and 8 feet.

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Example Question #3 : How To Find The Perimeter Of A Rectangle

Which of these polygons has the same perimeter as a rectangle with length 55 inches and width 15 inches?

Possible Answers:

A regular heptagon with sidelength two feet

A regular octagon with sidelength two feet

A regular hexagon with sidelength two feet

The other answer choices are incorrect.

A regular pentagon with sidelength two feet

Correct answer:

The other answer choices are incorrect.

Explanation:

The perimeter of a rectangle is twice the sum of its length and its width; a rectangle with dimensions 55 inches and 15 inches has perimeter

2 (55+15) = 140 inches.

All of the polygons in the choices are regular - that is, all have congruent sides - and all have sidelength two feet, or 24 inches, so we divide 140 by 24 to determine how many sides such a polygon would need to have a perimeter equal to the rectangle. However,

$140 \div 24 = 5 \frac{5}{6}$ ,

so there cannot be a regular polygon with these characteristics. All of the choices fail, so the correct response is that none are correct.

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Example Question #1 : How To Find The Perimeter Of A Parallelogram

The base length of a parallelogram is 4t+6 which is two times more than its side length. Give the perimeter of the parallelogram in terms of .

Possible Answers:

12t+9

12t+18

10t+18

8t+9

6t+9

Correct answer:

12t+18

Explanation:

The side length is half of the base length:

$h=\frac{w}{2}=\frac{4t+6}{2}=\frac{4t}{2}+\frac{6}{2}=2t+3$

The perimeter of a parallelogram is:

Perimeter=2(w+h)

Where:

is the base length of the parallelogram and is the side length

=2[(4t+6)+(2t+3)]

=2(6t+9)

=12t+18

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Example Question #2 : How To Find The Perimeter Of A Parallelogram

The side length of a parallelogram is t^2+1 and the base length is three times more than side length. Give the perimeter of the parallelogram in terms of .

Possible Answers:

8t^2+8

8t^2

4t^2+8

4t^2+4

8t^2+4

Correct answer:

8t^2+8

Explanation:

The base length is three times more than the side length, so we have:

Base length =3(t^2+1)=3t^2+3

The perimeter of a parallelogram is:

2(w+h)

Where:

is the base length of the parallelogram and is the side length. So we get:

$Perimeter=2(w+h)=2\left [ (3t^2+3)+(t^2+1) \right ]$

=2(4t^2+4)

=8t^2+8

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Example Question #1 : How To Find The Perimeter Of A Parallelogram

The base length of a parallelogram is 10 inches and the side length is 6 inches. Give the perimeter of the parallelogram.

Possible Answers:

Correct answer:

Explanation:

Like any polygon, the perimeter of a parallelogram is the total distance around the outside, which can be found by adding together the length of each side. In case of a parallelogram, each pair of opposite sides is the same length, so the perimeter is twice the base plus twice the side length. Or as a formula we can write:

Perimeter=2(w+h)

Where:

is the base length of the parallelogram and is the side length. So we can write:

Perimeter=2(w+h)=2(10+6)=32

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Example Question #1 : How To Find The Perimeter Of A Parallelogram

The base length of a parallelogram is t+2 . If the perimeter of the parallelogram is 24, give the side length in terms of .

Possible Answers:

20-t

22-2t

10-t

20+t

10+t

Correct answer:

10-t

Explanation:

Let:

Side length .

The perimeter of a parallelogram is:

2w+2h

where:

is the base length of the parallelogram and is the side length. The perimeter is known, so we can write:

Perimeter=24=2(t+2)+2x

Now we solve the equation for :

24=2(t+2)+2x

$\Rightarrow 24=2t+4+2x$

$\Rightarrow 24-2t-4=2x$

$\Rightarrow 20-2t=2x$

$\Rightarrow 10-t=x$

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Example Question #5 : How To Find The Perimeter Of A Parallelogram

The base length of a parallelogram is identical to its side length. If the perimeter of the parallelogram is 40, give the base length.

Possible Answers:

Correct answer:

Explanation:

The perimeter of a parallelogram is:

2(w+h)

Where:

is the base length of the parallelogram and is the side length. In this problem the base length and side length are identical, that means:

w=h

So we can write:

$Perimeter=40=2(w+w)\Rightarrow 20=2w\Rightarrow w=10$

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Example Question #841 : Geometry

The base length of a parallelogram is 2t+3 and the side length is 2t-3 . Give the perimeter of the parallelogram in terms of and calculate it for t=1 .

Possible Answers:

8t, 8

6t+6, 12

6t, 6

8t+8, 16

4t, 4

Correct answer:

8t, 8

Explanation:

The perimeter of a parallelogram is:

2(w+h)

where:

is the base length of the parallelogram and is the side length. So we have:

$Perimeter=2(w+h)=2\left [ (2t+3)+(2t-3) \right ]=2(4t)=8t$

and:

$t=1\Rightarrow 8t=8\times 1=8$

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Example Question #1061 : Ssat Upper Level Quantitative (Math)

Parallelogram1

The above parallelogram has area 100. Give its perimeter.

Possible Answers:

$20+20\sqrt{2}$

$20+20\sqrt{3}$

$40\sqrt{2}$

$40\sqrt{3}$

Correct answer:

$20+20\sqrt{2}$

Explanation:

The height of the parallelogram is , and the base is . By the $45^{\circ}-45^{\circ}-90^{\circ}$ Theorem, BD=CD . Since the product of the height and the base of a parallelogram is its area,

$BD \cdot CD = A$

$\left (BD \right )^{2} = 100$

BD = 10

By the $45^{\circ}-45^{\circ}-90^{\circ}$ Theorem,

CD = AB = BD = 10 , and

$AD = BC = BD \cdot \sqrt{2} = 10\sqrt{2}$

The perimeter of the parallelogram is

$AB + CD + BC + AD = 10 + 10 + 10\sqrt{2}+ 10\sqrt{2} = 20+20\sqrt{2}$

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SSAT Upper Level Math : Perimeter of Polygons

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #802 : Geometry

Example Question #803 : Geometry

Example Question #3 : How To Find The Perimeter Of A Rectangle

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #2 : How To Find The Perimeter Of A Parallelogram

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Example Question #5 : How To Find The Perimeter Of A Parallelogram

Example Question #841 : Geometry

Example Question #1061 : Ssat Upper Level Quantitative (Math)

All SSAT Upper Level Math Resources

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