SSAT Elementary Level Math : Plane Geometry

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

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Example Questions

Example Question #21 : Geometry

Find the area of the square shown below:

Screen shot 2015 11 03 at 3.19.10 pm

Possible Answers:

\displaystyle 20

\displaystyle 25

\displaystyle 24

\displaystyle 5

\displaystyle 10

Correct answer:

\displaystyle 25

Explanation:

A square has sides that are all equal. Area is length times width, and in the case of a square it is the side measurement times itself. \displaystyle 5\times5=25 

Example Question #22 : Geometry

Use the following to answer the question.

Square2

Find the area of the square.

Possible Answers:

\displaystyle 28\text{in}^2

\displaystyle 49\text{in}^2

\displaystyle 28\text{in}

\displaystyle 49\text{in}

\displaystyle \text{There is not enough information to find the area.}

Correct answer:

\displaystyle 49\text{in}^2

Explanation:

To find the area of a square, we use the following formula:

\displaystyle \text{area of square} = l \cdot w

where l is the width and w is the width of the square.

 

If we look at the square

Square2

we can see the width is 7in.  Because it is a square, we know that all sides are equal.  Therefore, the length is also 7in.  Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of square} = 7\text{in} \cdot 7\text{in}

\displaystyle \text{area of square} = 49\text{in}^2

Example Question #21 : Geometry

Use the following square to answer the question:

Square4

Find the area.

Possible Answers:

\displaystyle 8\text{in}^2

\displaystyle 4\text{in}^2

\displaystyle 2\text{in}^2

\displaystyle 10\text{in}^2

\displaystyle 6\text{in}^2

Correct answer:

\displaystyle 4\text{in}^2

Explanation:

To find the area of a square, we will use the following formula:

\displaystyle \text{area of square} = l \cdot w

where l is the length and w is the width of the square.

 

Now, let's look at the square.

Square4

We can see the width of the square is 2in.  Because it is a square, all sides are equal.  Therefore, the length is also 2in.

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of square} = 2\text{in} \cdot 2\text{in}

\displaystyle \text{area of square} = 4\text{in}^2

Example Question #23 : Squares

Use the following square to solve the problem:

Square1

Find the area.

Possible Answers:

\displaystyle 10\text{cm}^2

\displaystyle 20\text{cm}^2

\displaystyle 15\text{cm}^2

\displaystyle \text{There is not enough information to solve the problem.}

\displaystyle 25\text{cm}^2

Correct answer:

\displaystyle 25\text{cm}^2

Explanation:

To find the area of a square, we will use the following formula:

\displaystyle A = l \cdot w

where l is the length and w is the width of the square.

 

Now, given the square

Square1

we can see the length is 5cm.  Because it is a square, all sides are equal.  Therefore, the width is also 5cm.  So, we can substitute

\displaystyle A = 5\text{cm} \cdot 5\text{cm}

\displaystyle A = 25\text{cm}^2

Example Question #21 : Geometry

What is the perimeter of a square of area 36? 

Possible Answers:

\displaystyle 18

\displaystyle 36

\displaystyle 12

\displaystyle 6

\displaystyle 24

Correct answer:

\displaystyle 24

Explanation:

The area of a square is the square of the length of its side (all sides are equal in a square). If the area is 36, then the length of each side is 6. 

The perimeter of a square is 4 times the length of its side. Therefore, 4 times 6 is 24.

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

Which of the following is NOT a quadrilateral?

Possible Answers:

rhombus

trapezoid

parallelogram

nonagon

Correct answer:

nonagon

Explanation:

Quadrilaterals have 4 sides. A nonagon has 9 sides. 

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

What is the perimeter of a square that has a side measuring 3 inches in length? 

Possible Answers:

\displaystyle 12\ in

\displaystyle 9\ in

\displaystyle 6\ in

\displaystyle 3\ in

Correct answer:

\displaystyle 12\ in

Explanation:

Perimeter is the sum of all the sides. For a square, \displaystyle perimeter=side+side+side+side= 4\times side.

Therefore, for this square, 

\displaystyle perimeter=4\times 3\:in=12\:in.

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

What is the perimeter of a square that has a side measuring 1 inch in length? 

Possible Answers:

\displaystyle 1\ inch

\displaystyle 4\ inches

\displaystyle 2\ inches

\displaystyle 3\ inches

Correct answer:

\displaystyle 4\ inches

Explanation:

Perimeter is the sum of all the sides. For a square, \displaystyle perimeter=side+side+side+side=4 \times side.

Therefore, for this square, 

\displaystyle perimeter= 4 \times 1\:inch=4\:inches.

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

Screen_shot_2014-01-11_at_1.40.18_pm

What is the perimeter of the square?

Possible Answers:

\displaystyle 144

\displaystyle 101

\displaystyle 121

\displaystyle 88

\displaystyle 44

Correct answer:

\displaystyle 44

Explanation:

To find the perimeter of this square, add all four sides together. Even though we are only given one side's length, every side of a square always has the same length!

\displaystyle 11 + 11 + 11 + 11 = \mathbf{44}

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

Screen_shot_2014-02-20_at_9.16.17_pm

What is the perimeter of the square?

Possible Answers:

\displaystyle 14

\displaystyle 77

\displaystyle 70

\displaystyle 28

\displaystyle 49

Correct answer:

\displaystyle 28

Explanation:

To find the perimeter of a square, simply add all four sides together. Even though we are only given one side's length, squares always have four, equal sides!

\displaystyle 7 + 7 + 7 + 7 = 28

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