SSAT Middle Level Math : How to find the area of a rectangle

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

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Example Questions

Example Question #1 : How To Find The Area Of A Rectangle

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:

\displaystyle \$108

\displaystyle \$111

\displaystyle \$85

\displaystyle \$121

\displaystyle \$98

Correct answer:

\displaystyle \$108

Explanation:

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

Therefore, the total area Steve wants to cover is 

\displaystyle 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:

\displaystyle 968 \div 360 \approx 2.7

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

Example Question #2 : How To Find The Area Of A Rectangle

Rectangle

Give the area of the rectangle in the above diagram.

Possible Answers:

\displaystyle 80.64 \textrm{ cm}^2

\displaystyle 38\textrm{ cm}^2

\displaystyle 161.28 \textrm{ cm}^2

\displaystyle 76\textrm{ cm}^2

\displaystyle 40.32 \textrm{ cm}^2

Correct answer:

\displaystyle 80.64 \textrm{ cm}^2

Explanation:

The area of a rectangle is the product of its length and its height:

\displaystyle 12.6 \cdot6.4 = 80.64

The rectangle has a perimeter of 80.64 square centimeters.

Example Question #21 : Rectangles

 

Rectangle

Give the area of the rectangle in the above diagram.

Possible Answers:

\displaystyle 84 \textrm{ in}^2

\displaystyle 42 \textrm{ in}^2

\displaystyle 13 \frac{1}{10} \textrm{ in}^2

\displaystyle 26 \frac{1}{5} \textrm{ in}^2

\displaystyle 21 \textrm{ in}^2

Correct answer:

\displaystyle 42 \textrm{ in}^2

Explanation:

The area of a rectangle is the product of its length and its width:

\displaystyle 7 \frac{1}{2} \cdot 5 \frac{3}{5}

\displaystyle =\frac{7 \cdot 2 + 1}{2} \cdot \frac{5\cdot 5 + 3}{5}

\displaystyle =\frac{15}{2} \cdot \frac{28}{5} =\frac{3}{1} \cdot \frac{14}{1} = 42

The area of the rectangle is 42 square inches.

Example Question #1 : How To Find The Area Of A Rectangle

Prism

Give the surface area of the above box in square centimeters.

Possible Answers:

\displaystyle 324,000 \textrm { cm}^{2}

\displaystyle 28,800 \textrm { cm}^{2}

\displaystyle 32,400 \textrm { cm}^{2}

\displaystyle 216,000 \textrm { cm}^{2}

\displaystyle 21,600 \textrm { cm}^{2}

Correct answer:

\displaystyle 28,800 \textrm { cm}^{2}

Explanation:

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

\displaystyle 0.9 \times 100 = 90 centimeters

\displaystyle 0.6 \times 100 = 60 centimeters

Use the surface area formula, substituting \displaystyle L = 90, W = H = 60:

\displaystyle A = 2LH + 2LW + 2HW

\displaystyle A = 2 \cdot 90 \cdot 60 + 2\cdot 90 \cdot 60 + 2 \cdot 60 \cdot 60

\displaystyle A = 10,800 + 10,800 + 7,200 = 28,800 square centimeters

Example Question #316 : Ssat Middle Level Quantitative (Math)

Thingy

Above is a figure that comprises a red square and a white rectangle. The ratio of the length of the white rectangle to the sidelength of the square is \displaystyle 5:3. What percent of the entire figure is red?

Possible Answers:

\displaystyle 40 \%

\displaystyle 62.5 \%

\displaystyle 37.5 \%

\displaystyle 36 \%

\displaystyle 60 \%

Correct answer:

\displaystyle 37.5 \%

Explanation:

To make this easier, we will assume that the rectangle has length 5 and the square has sidelength 3. Then the area of the entire figure is 

\displaystyle (3 + 5) \times 3 = 24,

and the area of the square is 

\displaystyle 3 \times 3 = 9

The square, therefore, takes up

\displaystyle \frac{9}{24} \times 100 = \frac{900}{24} = 37.5 \%

of the entire figure.

Example Question #1 : How To Find The Area Of A Rectangle

https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/problem_question_image/image/2333/Q_3.png

The rectangle above is \displaystyle 5 inches long and \displaystyle 10 inches wide. What is the area of the rectangle?

Note: Figure not drawn to scale.

Possible Answers:

\displaystyle 30\: in^{2}

\displaystyle 15\: in

\displaystyle 50\: in^{2}

\displaystyle 30\: in

\displaystyle 50\: in

Correct answer:

\displaystyle 50\: in^{2}

Explanation:

The area of the rectangle is \displaystyle 50\: in^{2}. In order to find the area of a rectangle, multiply the length (5 inches) by the width (10 inches). The answer is in units2 because the area, by definition, is the number of square units that cover the inside of a figure.

Example Question #1 : How To Find The Area Of A Rectangle

Swimming_pool

The above depicts a rectangular swimming pool for an apartment. The pool is two meters deep everywhere. What is the volume of the pool in cubic meters?

Possible Answers:

\displaystyle 1,440\textrm{ m}^{3}

\displaystyle 876\textrm{ m}^{3}

\displaystyle 720 \textrm{ m}^{3}

The correct answer is not among the other choices.

\displaystyle 820\textrm{ m}^{3}

Correct answer:

\displaystyle 720 \textrm{ m}^{3}

Explanation:

The pool can be seen as a rectangular prism with dimensions 24 meters by 15 meters by 2 meters; its volume is the product of these dimensions, or

\displaystyle 24 \times 15 \times 2 = 720 cubic meters.

Example Question #4 : Geometry

Rectangles

Note: Figure NOT drawn to scale.

What percent of the above figure is white?

Possible Answers:

\displaystyle 18 \frac{3}{4} \%

\displaystyle 22 \frac{1}{2} \%

\displaystyle 20 \%

\displaystyle 17 \frac{1}{2} \%

\displaystyle 25 \%

Correct answer:

\displaystyle 18 \frac{3}{4} \%

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 white region is 

\displaystyle \frac{600}{3,200} \times 100 = 18 \frac{3}{4} \%

of the large rectangle.

Example Question #1 : Geometry

What is the area of a rectangle with length \displaystyle 14\ cm and width \displaystyle 12\ cm?

Possible Answers:

\displaystyle 158\;cm^{2}

\displaystyle 168\;cm^{2}

\displaystyle 198\;cm^{2}

\displaystyle 144\; cm^{2}

\displaystyle 148\; cm^{2}

Correct answer:

\displaystyle 168\;cm^{2}

Explanation:

The formula for the area, \displaystyle A, of a rectangle when we are given its length, \displaystyle L, and width, \displaystyle W, is \displaystyle A = L * W.

To calculate this area, just multiply the two terms.

\displaystyle A = 14\ cm * 12\ cm = 168\; cm^{2}

Example Question #321 : Ssat Middle Level Quantitative (Math)

Order the following from least area to greatest area:

Figure A: A rectangle with length 10 inches and width 14 inches.

Figure B: A square with side length 1 foot.

Figure C: A triangle with base 16 inches and height 20 inches.

Possible Answers:

\displaystyle B, C, A

\displaystyle A, B, C

\displaystyle B, A, C

\displaystyle C,A, B

\displaystyle A, C, B

Correct answer:

\displaystyle A, B, C

Explanation:

Figure A has area \displaystyle 10 \times 14 = 140 square inches.

Figure B has area \displaystyle 12 \times 12 = 144 square inches, 1 foot being equal to 12 inches.

Figure C has area \displaystyle \frac{1}{2} \times 16 \times 20 = 160 square inches.

The figures, arranged from least area to greatest, are A, B, C.

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