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SSAT Upper Level Math : Areas and Perimeters of Polygons

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Example Questions

Example Question #101 : Areas And Perimeters Of Polygons

Parallelogram

Figure NOT drawn to scale.

The above depicts Rhombus ABCD , which has perimeter 80. XC = 16 .

Give the area of Rhombus ABCD .

Possible Answers:

256

400

320

Correct answer:

320

Explanation:

The area of any parallelogram is the product of the length of its base and that of a corresponding altitude. We can take $\overline{CD}$ as a base and perpendicular $\overline{XC}$ as an altitude.

All four sides of a rhombus have the same length, so we can find by dividing the perimeter - the sum of the lengths of the four sides - by 4:

$CD = p \div 4 = 80 \div 4 = 20$

Now multiply the lengths of this base and the altitude to get the area:

$a = CD \cdot XC = 20 \cdot 16 = 320$

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Example Question #3 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

What two shapes can a square be classified as?

Possible Answers:

Trapezoid and Triangle

Rhombus and Triangle

Trapezoid and Rhombus

Rectangle and Rhombus

Rectangle and Triangle

Correct answer:

Rectangle and Rhombus

Explanation:

A square can also be a rectangle and a rhombus because a rectangle has to have at least sets of equal side lengths and a rhombus has to have equal side lengths, like a square, and at least sets of equal angles.

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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 #3 : 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 #1061 : Ssat Upper Level Quantitative (Math)

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

20-t

10-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 #6 : How To Find The Perimeter Of A Parallelogram

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:

6t, 6

6t+6, 12

4t, 4

8t, 8

8t+8, 16

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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Example Question #41 : Perimeter Of Polygons

Parallelogram2

Give the perimeter of the above parallelogram if BD = 10 .

Possible Answers:

$40+20\sqrt{2}$

$40+40\sqrt{3}$

$60\sqrt{2}$

$40+20\sqrt{3}$

$60\sqrt{3}$

Correct answer:

$40+20\sqrt{3}$

Explanation:

By the $30^{\circ}-60^{\circ}-90^{\circ}$ Theorem:

$AB = CD= BD\sqrt{3}= 10\sqrt{3}$ , and

$AD=BC= 2\cdot BD = 2\cdot 10 = 20$

The perimeter of the parallelogram is

$AB + CD + BC + AD = 20+20+ 10\sqrt{3}+ 10\sqrt{3} = 40+20\sqrt{3}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Areas and Perimeters of Polygons

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #101 : Areas And Perimeters Of Polygons

Example Question #3 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

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

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

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

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

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

Example Question #6 : How To Find The Perimeter Of A Parallelogram

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

Example Question #41 : Perimeter Of Polygons

All SSAT Upper Level Math Resources

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