SSAT Middle Level Math : Geometry

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

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Example Questions

Example Question #74 : Quadrilaterals

The length of a rectangle is three times longer than its width. If the width of the rectangle is \(\displaystyle 3\) meters, give the area of the rectangle.

Possible Answers:

\(\displaystyle 21\ m^2\)

\(\displaystyle 24\ m^2\)

\(\displaystyle 27\ m^2\)

\(\displaystyle 33\ m^2\)

\(\displaystyle 30\ m^2\)

Correct answer:

\(\displaystyle 27\ m^2\)

Explanation:

The length of the rectangle would be: \(\displaystyle 3\times 3=9\ m\)

 

We know that:

 

\(\displaystyle Area=a\times b\)

 

where:

 

\(\displaystyle a=Length \ of\ the\ rectangle\)

\(\displaystyle b= Width\ of\ the\ rectangle\)

 

So we can write:

 

\(\displaystyle Area=9\times 3=27\ m^2\)

Example Question #173 : Plane Geometry

Which of the following is the area of a rectangle with a width of 4 feet and a length that is twice the width?

Possible Answers:

\(\displaystyle 34\ \text{ft}^2\)

\(\displaystyle 32\ \text{ft}^2\)

\(\displaystyle 64\ \text{ft}^2\)

\(\displaystyle 36\ \text{ft}^2\)

\(\displaystyle 16\ \text{ft}^2\)

Correct answer:

\(\displaystyle 32\ \text{ft}^2\)

Explanation:

The area of a rectangle is found by multiplying the width by the length.

\(\displaystyle A=w\times l\)

We know that the width is 4 feet and the the length must be twice the width. Multiply the width by 2 to find the length.

\(\displaystyle l=2\times4=8\)

Multiply the length and width to find the area.

\(\displaystyle 4\times8=32\)

Example Question #331 : Ssat Middle Level Quantitative (Math)

Jeff decided to build a play area for his guinea pigs. The play area would be an enclosure 6 feet long, 2 feet wide, and 2 feet tall. In cubic feet, how big is the play area?

Possible Answers:

\(\displaystyle 24\ ft^{3}\)

\(\displaystyle 12\ ft^{3}\)

\(\displaystyle 16\ ft^{3}\)

\(\displaystyle 18\ ft^{3}\)

Correct answer:

\(\displaystyle 24\ ft^{3}\)

Explanation:

The cubic feet of an area is found by multiping the length times the width times the height. Given that the length is six feet, the width is two feet, and that the height is two feet, the total cubic area would be found using this equation:

\(\displaystyle length\cdot width \cdot heighth\)

Here is the equation with the appropriate numbers plugged in:

\(\displaystyle 6\cdot 2\cdot 2 = 24\)

Therefore, 24 cubic feet is the correct answer. 

Example Question #4 : Geometry

Jessica's blanket is 12 square feet. Lisa has a blanket that is half the size of Jessica's blanket. Which of the following are possible dimensions of Lisa's blanket?

Possible Answers:

\(\displaystyle 2\ ft\times2\ ft\)

\(\displaystyle 3\ ft\times3\ ft\)

\(\displaystyle 1\ ft\times12\ ft\)

\(\displaystyle 3\ ft\times2\ ft\)

Correct answer:

\(\displaystyle 3\ ft\times2\ ft\)

Explanation:

The area of a rectangle if found by multiplying the length times the width. Here, we know that Lisa's blanket is half the area of Jessica's blanket. Since Jessica's blanket is 12 square feet, that means that Lisa's blanket must be 6 square feet. 

The only length and width values that give us 6 square feet when multiplied by one another are 3 feet by 2 feet. This is therefore the correct answer. 

Example Question #2001 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Rectangles

Note: Figure NOT drawn to scale.

What percent of the above figure is red?

Possible Answers:

The correct answer is not given among the other choices.

\(\displaystyle 75 \%\)

\(\displaystyle 87 \frac{1}{2} \%\)

\(\displaystyle 66 \frac{2}{3} \%\)

\(\displaystyle 90 \%\)

Correct answer:

The correct answer is not given among the other choices.

Explanation:

The large rectangle has length 80 and width 40, and, consequently, area

\(\displaystyle 80 \times 40 = 3,200\).

The white region is a rectangle with length 30 and width 20, and, consequently, area 

\(\displaystyle 30 \times 20 = 600\).

The red region, therefore, has area \(\displaystyle 3,200 - 600 = 2,600\)

The red region is 

\(\displaystyle \frac{2,600}{3,200} \times 100 = 81 \frac{1}{4} \%\)

of the large rectangle.

This is not one of the choices.

Example Question #173 : Plane Geometry

Rectangles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the area of the red region to that of the white region.

Possible Answers:

\(\displaystyle 7:1\)

\(\displaystyle 3:1\)

\(\displaystyle 25:7\)

The correct answer is not given among the other choices.

\(\displaystyle 13:3\)

Correct answer:

\(\displaystyle 13:3\)

Explanation:

The large rectangle has length 80 and width 40, and, consequently, area

\(\displaystyle 80 \times 40 = 3,200\).

The white region is a rectangle with length 30 and width 20, and, consequently, area 

\(\displaystyle 30 \times 20 = 600\).

The red region, therefore, has area \(\displaystyle 3,200 - 600 = 2,600\)

The ratio of the area of the red region to that of the white region is 

\(\displaystyle \frac{2,600}{600} = \frac{2,800 \div 200}{600\div 200 }= \frac{13}{3}\)

That is, 13 to 3.

Example Question #43 : Rectangles

Swimming_pool

The above figure depicts the rectangular swimming pool at an apartment. The apartment manager needs to purchase a tarp that will cover this pool completely, but the store will only sell the material in multiples of one hundred square meters. How many square meters will the manager need to buy?

Possible Answers:

\(\displaystyle 500\textrm{ m}^{2}\)

\(\displaystyle 300\textrm{ m}^{2}\)

\(\displaystyle 400\textrm{ m}^{2}\)

Insufficient information is given to answer the question.

\(\displaystyle 600\textrm{ m}^{2}\)

Correct answer:

\(\displaystyle 400\textrm{ m}^{2}\)

Explanation:

The tarp needed to cover this pool must be, at minimum, the product of its length and width, or

\(\displaystyle 24 \times 15 = 360\) square meters. 

The manager will need to buy a number of square yards of tarp equal to the next highest multiple of one hundred, which is 400 square meters.

Example Question #51 : Rectangles

The four angles of a square are labeled A, B, C, and D. What is the sum of \(\displaystyle A+B+C\)?

Possible Answers:

\(\displaystyle 300^o\)

\(\displaystyle 180^o\)

More information is needed to solve

\(\displaystyle 90^o\)

\(\displaystyle 270^o\)

Correct answer:

\(\displaystyle 270^o\)

Explanation:

In a square, each angle is 90 degrees.

\(\displaystyle A=B=C=D=90^o\)

We can plug in 90 for each variable and find the sum.

\(\displaystyle A+B+C=90^o+90^o+90^o=270^o\)

Example Question #24 : How To Find The Area Of A Rectangle

Swimming_pool

The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. 

An apartment manager wants to paint the four sides and the bottom of the swimming pool. How many square feet will he need to paint?

Possible Answers:

The correct answer is not given among the other responses.

\(\displaystyle 10,500 \textrm{ ft}^{2}\)

\(\displaystyle 4,520 \textrm{ ft}^{2}\)

\(\displaystyle 2,770 \textrm{ ft}^{2}\)

\(\displaystyle 1,020 \textrm{ ft}^{2}\)

Correct answer:

\(\displaystyle 2,770 \textrm{ ft}^{2}\)

Explanation:

The bottom of the swimming pool has area 

\(\displaystyle 50 \times 35 = 1,750\) square feet.

There are two sides whose area is 

\(\displaystyle 50 \times 6 = 300\) square feet,

and two sides whose area is 

\(\displaystyle 35 \times 6 = 210\) square feet.

Add the areas:

\(\displaystyle 1,750 + 300 + 300 + 210 +210=2,770\) square feet.

Example Question #25 : How To Find The Area Of A Rectangle

If the angles of a quadrilateral are equal to \(\displaystyle b\), \(\displaystyle 2b\), \(\displaystyle 3b\), and \(\displaystyle 3b\), what is the value of \(\displaystyle b\)?

Possible Answers:

\(\displaystyle 40\)

\(\displaystyle 50\)

\(\displaystyle 70\)

\(\displaystyle 60\)

Correct answer:

\(\displaystyle 40\)

Explanation:

Given that there are 360 degrees in a quadrilateral, 

\(\displaystyle b+2b+3b+3b=360\)

\(\displaystyle 9b=360\)

\(\displaystyle b=40\)

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