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SSAT Middle Level Math : Geometry

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

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All SSAT Middle Level Math Resources

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Example Questions

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Example Question #5 : How To Find A Square On A Coordinate Plane

A square has an area of 121 square units, what is the perimeter of the square?

Possible Answers:

120

Correct answer:

Explanation:

In order to solve this problem, apply the formula A=S^2 , in order to conclude that the length of side must equal for the area to equal 121 .

Once you've found the length of side , apply the formula P=4S

$P=4\times11=44$

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Example Question #31 : Coordinate Geometry

A square has an area of 144 square units. Find the perimeter.

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, apply the formula A=S^2 , in order to conclude that the length of side must equal for the area to equal 144 .

Once you've found the length of side , apply the formula P=4S

$P=4\times12=48$

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Example Question #1 : How To Find A Square On A Coordinate Plane

Vt_custom_xy_xy_ss_square1

Find the area of the above square.

Possible Answers:

36 units^2

28 units^2

30 units^2

42 units^2

Correct answer:

36 units^2

Explanation:

In order to find the area of the square above apply the formula: A=S^2 , where the length of one side of the square.

Since S=6 ,
the solution is $A=6^2=6\times6=36$

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Example Question #8 : How To Find A Square On A Coordinate Plane

Vt_custom_xy_xyss2

Find the area of the square shown above.

Possible Answers:

110 units^2

100 units^2

100

125 units^2

Correct answer:

100 units^2

Explanation:

In order to find the area of the above square, apply the formula: A=S^2 , when equals the length of one side of the square.

Since, S=10 the solution is:

$A=10^2=10\times10=100$

Make sure to attach "square units" to your answer!

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Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Parellelogram

NOTE: Figure NOT drawn to scale.

What is the area of the parallelogram represented by the above figure?

Possible Answers:

144

112

Correct answer:

Explanation:

The area of a parallelogram is its base multiplied by its height. The diagram below shows both in green:

Parellelogram

$A = 9 \cdot5 = 45$

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Example Question #31 : Geometry

Triangle5

Find the area of the above parallelogram given a height of 5 units, as shown to scale.

Possible Answers:

$25 \text{ square units}$

$15 \text{ square units}$

$30 \text{ square units}$

$12.5 \text{ square units}$

Correct answer:

$30 \text{ square units}$

Explanation:

Since the diagram is drawn to scale, the base of the parallelogram must be 6 units in length. Using the area formula for a parallelogram:

$A = base \times height = 6 \times 5 = 30$

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Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Triangle5

Given a base of 12 units and an area of 120 square units, find the height of the paralellogram shown above.

Possible Answers:

$\sqrt{10}$

Correct answer:

Explanation:

The area formula for a parallelogram is:

$A = base \times height$

Thus, to find the height, rearrange:

$height = \frac{A}{base} = \frac{120}{12} = 10$

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Example Question #32 : Geometry

Triangle5

The above parallelogram has an area of 30 square units. Which of the following could be the lengths of the base and height of this figure? (Image not drawn to scale.)

Possible Answers:

7, 6

4, 8

3, 10

5, 5

Correct answer:

3, 10

Explanation:

The formula for the area of a parallelogram is:

$A = base \times height$

Thus, the base and height must equal 30 square units when multiplied together.

3 and 10 are the only combination of base and height which, when multiplied, equal the area of 30 square units.

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Example Question #1 : How To Find A Rectangle On A Coordinate Plane

Custom_vt_xy_gif_file_12

In the above figure Dr. Robinson's shed is represented by the red square, and the shed has a perimeter of $\small 12$ yards. Find how much area Dr. Robinson has in his backyard--excluding the area that the shed occupies.

Possible Answers:

$\small 110$ $\small yards^2$

$\small 129$ $\small yards^2$

$\small 120$ $\small yards^2$

$\small \small 111$ $\small yards^2$

Correct answer:

$\small \small 111$ $\small yards^2$

Explanation:

To find how much area Dr. Robinson has around his shed in his backyard, first apply the formula: $\small \small P=4S$ , where $\small S$ represents one side of the red shed. Given that $\small \small P=12$
$\small S$ must equal $\small 3$ because $\small 4\times3=12$ .

Now you have enough information to find the area of the red shed.
Apply the formula: $\small A=S^2$
$\small A=3^2=3\times3=9$

Since the rectangular fence has a width of $\small 15$ yards and a length of $\small 8$ yards, apply the formula: $\small Area=width\times length$ in order to find the area of the entire backyard.
Thus,
$\small Area=15\times8=120$

Then simply find the difference between the area of the entire yard and the area of the shed.

Thus the final solution is:
$\small 120-9=111$

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Example Question #1 : How To Find A Rectangle On A Coordinate Plane

Custom_vt_xy_gif_file_13abcd

Identify the correct set of coordinates for rectangle $\small ABCD$ .

Possible Answers:

$\small (11,3),(-10,7),(3,3),(3,7)$

$\small (-11,3),(-11,7),(3,3),(3,7)$

$\small (-11,3),(-11,7),(-3,-3),(3,7)$

$\small (-11,3),(11,7),(3,3),(-3,7)$

Correct answer:

$\small (-11,3),(-11,7),(3,3),(3,7)$

Explanation:

To identify the correct set of coordinate points for rectangle $\small ABCD$ , note that the correct set must have two sets of matching $\small x$ coordinates and two sets of matching $\small y$ coordinates. The only answer choice that meets these specifications is: $\small \small (-11,3),(-11,7),(3,3),(3,7)$

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SSAT Middle Level Math : Geometry

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #5 : How To Find A Square On A Coordinate Plane

Example Question #31 : Coordinate Geometry

Example Question #1 : How To Find A Square On A Coordinate Plane

Example Question #8 : How To Find A Square On A Coordinate Plane

Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Example Question #31 : Geometry

Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Example Question #32 : Geometry

Example Question #1 : How To Find A Rectangle On A Coordinate Plane

Example Question #1 : How To Find A Rectangle On A Coordinate Plane

All SSAT Middle Level Math Resources

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