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

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

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Example Questions

Example Question #51 : Plane Geometry

What is the area of a square with perimeter 64 inches?

Possible Answers:

$1,024 \; \textrm{in}^{2}$

$512 \; \textrm{in}^{2}$

$4,096 \; \textrm{in}^{2}$

$256 \; \textrm{in}^{2}$

It cannot be determined from the information given.

Correct answer:

$256 \; \textrm{in}^{2}$

Explanation:

The perimeter of a square is four times its sidelength, so a square with perimeter 64 inches has sides with length 16 inches. Use the area formula:

$A = s^{2} = 16^{2} = 256$

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Example Question #52 : Plane Geometry

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Possible Answers:

Correct answer:

Explanation:

A square that has an area of 81 has sides that are the square root of 81 (side² = area for a square). Thus each of the four sides is 9. The sum of three of these sides is 9 + 9 + 9 = 27 .

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Example Question #11 : Quadrilaterals

Cube

What is the total area of the surface of the cube shown in the above diagram?

Possible Answers:

$42 \textrm{ in}^{2}$

$42 \frac{7}{8} \textrm{ in}^{2}$

$62 \frac{1}{2} \textrm{ in}^{2}$

$49 \textrm{ in}^{2}$

$73 \frac{1}{2} \textrm{ in}^{2}$

Correct answer:

$73 \frac{1}{2} \textrm{ in}^{2}$

Explanation:

A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:

$3 \frac{1}{2} \times 3 \frac{1}{2} = \frac{7}{2} \times \frac{7}{2} = \frac{49}{4} \textrm{ in}^{2}$

Then multiply this by six:

$6 \times \frac{49}{4} =\frac{6}{1} \times \frac{49}{4} = \frac{3}{1} \times \frac{49}{2} = \frac{147}{2} = 73 \frac{1}{2} \textrm{ in}^{2}$

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Example Question #54 : Plane Geometry

Cube

What is the total area of the surface of the cube shown in the above diagram?

Possible Answers:

$31.2\textrm{ cm}^{2 }$

$27.04 \textrm{ cm}^{2}$

$40.56 \textrm{ cm}^{2}$

$105.456 \textrm{ cm}^{2}$

$17.576 \textrm{ cm}^{2}$

Correct answer:

$40.56 \textrm{ cm}^{2}$

Explanation:

A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:

$2.6 \times 2.6 = 6.76 \textrm{ cm}^{2}$

Then multiply this by six:

$6 \times 6.76 = 40.56 \textrm{ cm}^{2}$

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Example Question #21 : Quadrilaterals

Cube

What is the total area of the surface of the cube shown in the above diagram?

Possible Answers:

$3,750\textrm{ in}^{2}$

$625\textrm{ in}^{2}$

$2,500\textrm{ in}^{2}$

$15,625\textrm{ in}^{2}$

$5,000\textrm{ in}^{2}$

Correct answer:

$3,750\textrm{ in}^{2}$

Explanation:

A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:

$25 \times 25 = 625 \textrm{ in}^{2}$

Then multiply this by six:

$6 \times 625 = 3,750\textrm{ in}^{2}$

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Example Question #4 : How To Find The Area Of A Square

Cube

What is the total area of the surface of the cube shown in the above diagram?

Possible Answers:

$144 \textrm{ cm}^2$

$864 \textrm{ cm}^2$

$1,728 \textrm{ cm}^2$

$288 \textrm{ cm}^2$

$576 \textrm{ cm}^2$

Correct answer:

$864 \textrm{ cm}^2$

Explanation:

A cube comprises six faces, each of which is a square. To find its total surface area, find the area of one face by squaring its sidelength:

$12 \times 12 = 144 \textrm{ cm}^{2}$

Then multiply this by six:

$6 \times 144 = 864\textrm{ cm}^{2}$

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Example Question #5 : Geometry

A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Possible Answers:

Correct answer:

Explanation:

Each side can be divided into three 3-foot sections. This gives a total of $3\times3=9$ squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.

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Example Question #6 : How To Find The Area Of A Square

Order the following from least area to greatest area:

Figure A: A square with sides of length 3 feet each.

Figure B: A rectangle with length 30 inches and width 42 inches.

Figure C: A rectangle with length 2 feet and width 4 feet.

Possible Answers:

A, B, C

A, C, B

B, C,A

C, A, B

C, B, A

Correct answer:

C, B, A

Explanation:

Figure A has area $3 ^{2} = 3 \times 3 = 9$ square feet.

Figure B has dimensions $30 \div12 = 2 \frac{1}{2}$ feet by $42 \div12 = 3 \frac{1}{2}$ feet, so its area is

$2 \frac{1}{2} \times 3 \frac{1}{2} = \frac{5}{2} \times \frac{7}{2} = \frac{35}{4} = 8 \frac{3}{4}$ square feet.

Figure C has area $2 \times 4 = 8$ square feet.

From least area to greatest, the figures rank C, B, A.

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Example Question #7 : How To Find The Area Of A Square

The length of one side of a square is $11\: cm$ . What is the square's area?

Possible Answers:

$44\: cm$

$121\: cm$

$121\: cm^{2}$

$44\: cm^{2}$

Correct answer:

$121\: cm^{2}$

Explanation:

The area of any quadrilateral is found by multiplying the length by the width. Because a square has four equal sides, the length and width are the same. For the square in this question, the length and width are $11\: cm$ .

Remember: area is always given in units² .

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

If a square has a side that is 3 yards long, what is the area in square feet?

Possible Answers:

$81\ \text{ft}^2$

$9\ \text{ft}^2$

$21\ \text{ft}^2$

$27\ \text{ft}^2$

$30\ \text{ft}^2$

Correct answer:

$81\ \text{ft}^2$

Explanation:

The area of a square is found by multiplying the length of a side by itself.

$A=s\times s=s^2$

If one side is 3 yards, this means one side is 9 feet since there are 3 feet in a yard.

$3\ \text{yards}\times3\ \text{feet per yard}=9\ \text{feet}$

Since every side is of equal length, you would multiply 9 feet by 9 feet to find the area.

$A=s\times s$

s=9

$A=9\times9=81$

This results in 81 square feet, which is the correct answer.

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

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #51 : Plane Geometry

Example Question #52 : Plane Geometry

Example Question #11 : Quadrilaterals

Example Question #54 : Plane Geometry

Example Question #21 : Quadrilaterals

Example Question #4 : How To Find The Area Of A Square

Example Question #5 : Geometry

Example Question #6 : How To Find The Area Of A Square

Example Question #7 : How To Find The Area Of A Square

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

All SSAT Middle Level Math Resources

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