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SSAT Middle Level Math : Quadrilaterals

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Example Questions

Example Question #11 : Rectangles

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the perimeter of the red polygon.

Possible Answers:

120

240

140

340

The perimeter cannot be determined from the information given.

Correct answer:

240

Explanation:

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

Rectangles

The sidelengths of the red polygon can now be added to find the perimeter:

40 + 80 + 20 + 30 + 20 + 50 = 240

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Example Question #74 : Plane Geometry

The width of a rectangle is , the length is , and the perimeter is 72. What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Start with the equation for the perimeter of a rectangle:

P=l+l+w+w=2l+2w

We know the perimeter is 72, the length is , and the width is . Plug these values into our equation.

72=2(6x)+2(3x)

Multiply and combine like terms.

72=12x+6x

72=18x

Divide by 18 to isolate the variable.

$\frac{72}{18}=x$

Simplify the fraction by removing the common factor.

$\frac{72}{18}=\frac{72\div18}{18\div18}=\frac{4}{1}=4$

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Example Question #41 : Quadrilaterals

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the perimeter of the large rectangle to that of the smaller rectangle.

Possible Answers:

12:5

8:3

2:1

16:7

The correct answer is not given among the other choices.

Correct answer:

12:5

Explanation:

Opposite sides of a rectangle are congruent.

The large rectangle has perimeter

40 + 80 + 40 + 80 = 240 .

The smaller rectangle has perimeter

20 + 30 + 20 + 30 = 100 .

The ratio is

$\frac{240}{100} = \frac{240 \div 20 }{100\div 20 } = \frac{12}{5}$ ; that is, 12 to 5.

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Example Question #41 : Quadrilaterals

What is the perimeter of a rectangle with a width of 3 and a length of 10?

Possible Answers:

Correct answer:

Explanation:

The formula for the perimeter of a rectangle is $\dpi{100} Perimeter=2l+2w$ .

Plug in our given values to solve:

$\dpi{100} Perimeter = 2(20)+2(3)$

$\dpi{100} Perimeter = 20+6$

$\dpi{100} Perimeter = 26$

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Example Question #81 : Plane Geometry

Rectangle ABCD has an area of . If the width of the rectangle is , what is the perimeter?

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is found by multiplying the length times the width. The question tells you the width is and the area is .

Thus the length is 8. $\left ( 40 \div5\right)$ .

To find the perimeter you add up all of the sides.

length+length+width+width=perimeter

8 + 8 + 5 + 5 = 26

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Example Question #2 : How To Find The Perimeter Of The Rectangle

If the perimeter of a rectangle is inches and the width is inches, what is the length?

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle is represented by the following formula, in which W represents width and L represents length:

2W+2L= Perimeter

Given that the width is inches and that the perimeter is inches, the following applies:

$2\cdot 2+2L=14$

4+2L=14

Next, subtract from each side.

2L=10

Now, divide each side by .

This gives us

L=5

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Example Question #82 : Plane Geometry

A rectangle has an area of . The length of each side is a whole number. What is NOT a possible value for the rectangle's perimeter?

Possible Answers:

Correct answer:

Explanation:

Since each side is a whole number, first find the whole number factors of . They are and , and , and , and and . These sidelengths correspond to perimeters of , , , and , respectively. Thus, is answer.

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Example Question #311 : Ssat Middle Level Quantitative (Math)

Rectangle

Give the perimeter of the above rectangle in centimeters, using the conversion factor 91.44 centimeters per yard.

Possible Answers:

$1,097.28 \textrm{ cm}$

$4,389.12 \textrm{ cm}$

$2,011.68 \textrm{ cm}$

$1,005.84 \textrm{ cm}$

$2,194.56 \textrm{ cm}$

Correct answer:

$2,011.68 \textrm{ cm}$

Explanation:

The perimeter of the rectangle is 8 + 3 + 8 + 3 = 22 yards. To convert this to centimeters, multiply by the given conversion factor:

$91.44 \times 22 = 2,011.68$ centimeters.

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Example Question #312 : Ssat Middle Level Quantitative (Math)

Find the perimeter of the rectangle shown below

Screen shot 2015 11 10 at 9.55.29 pm

Possible Answers:

Correct answer:

Explanation:

The perimeter of a rectangle, or any shape, is the distance around the outside. You add up the length of each side to find this number. The coordinates of the points are (-3,8)(5,8)(5,-2)(-3,-2) . You need to find the distance between each point. The short side is units, and the longer side is units.

$(8\times2)+(10\times2)=16+20=36$

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Example Question #83 : Plane Geometry

Steve's bedroom measures 20' by 18' by 8' high. He wants to paint the ceiling and all four walls using a paint that gets 360 square feet of coverage per gallon. A one-gallon can of the paint Steve wants costs $36.00; a one-quart can costs $13.00. What is the least amount of money that Steve can expect to spend on paint in order to paint his room?

Possible Answers:

$\$98$

$\$111$

$\$121$

$\$108$

$\$85$

Correct answer:

$\$108$

Explanation:

Two of the walls have area $20 \cdot 8 = 160\;\textrm{in}^{2}$ ; two have area $18 \cdot 8 = 144\;\textrm{in}^{2}$ ; the ceiling has area $20 \cdot 18 = 360\;\textrm{in}^{2}$ .

Therefore, the total area Steve wants to cover is

$A = 160 + 160 + 144 + 144 + 360 =968 \; \textrm{in}^{2}$

Divide 968 by 360 to get the number of gallons Steve needs to paint his bedroom:

$968 \div 360 \approx 2.7$

Since $2 \frac{1}{2} < 2.7 < 2\frac{3}{4}$ , Steve needs to purchase either two gallon cans and three quart cans, or three gallon cans.

The first option will cost him $36 \cdot2 + 13 \cdot3 = \$111$ ; the second option will cost him $36 \cdot3 = \$108$ . The latter is the more economical option.

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SSAT Middle Level Math : Quadrilaterals

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #11 : Rectangles

Example Question #74 : Plane Geometry

Example Question #41 : Quadrilaterals

Example Question #41 : Quadrilaterals

Example Question #81 : Plane Geometry

Example Question #2 : How To Find The Perimeter Of The Rectangle

Example Question #82 : Plane Geometry

Example Question #311 : Ssat Middle Level Quantitative (Math)

Example Question #312 : Ssat Middle Level Quantitative (Math)

Example Question #83 : Plane Geometry

All SSAT Middle Level Math Resources

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