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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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Example Questions

Example Question #221 : Ssat Middle Level Quantitative (Math)

Triangle5

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

Possible Answers:

$12.5 \text{ square units}$

$25 \text{ square units}$

$15 \text{ square units}$

$30 \text{ square units}$

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 #222 : Ssat Middle Level Quantitative (Math)

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 #223 : Ssat Middle Level Quantitative (Math)

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:

4, 8

3, 10

7, 6

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 #221 : Ssat Middle Level Quantitative (Math)

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:

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

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

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

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

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 #222 : Ssat Middle Level Quantitative (Math)

Custom_vt_xy_gif_file_13abcd

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

Possible Answers:

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

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

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

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

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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Example Question #223 : Ssat Middle Level Quantitative (Math)

Dr. Robinson recently put a rectangular fence around his backyard. The fence has a width of $\small 15$ yards and a length of $\small 8$ yards. If Dr. Robinson paid $\small \small \$ 12.50$ for every yard of fence, how much did the fence cost?

Possible Answers:

$\small \$625$

$\small \$575$

$\small \$525$

$\small \$375$

Correct answer:

$\small \$575$

Explanation:

To find the cost of the fence, apply the formula $\small P=2(width)+2(length)$ in order to first find the length of the perimeter of the fence.

Then multiply the perimeter by $\small \$12.50$ .

Thus, the solution is:

$\small P=2(15)+2(8)$
$\small P=30+16$
$\small P=46$

$\small 46\times12.5=575$

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Example Question #224 : Ssat Middle Level Quantitative (Math)

Custom_vt_xy_gif_file_13abcd

The rectangle shown above has a width of $\small 14$ and a length of $\small 4$ . Find the area and perimeter of the rectangle.

Possible Answers:

$\small \small A=56 units^2, P=36$

$\small \small A=50 units^2, P=34$

$\small \small A=36 units^2, P=36$

$\small \small A=43 units^2, P=26$

Correct answer:

$\small \small A=56 units^2, P=36$

Explanation:

To solve this problem apply the formulas: $\small Area=width\times length$ & $\small Perimeter=2(w)+2(l)$

Thus, the solution is:

$\small A=14\times4=56$
$\small P=2(14)+2(4)=28+8=36$

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Example Question #1 : Triangles

A right triangle has legs 90 centimeters and 16 centimeters, What is its area?

Possible Answers:

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

$4,050 \; \textrm{cm}^{2}$

$405\; \textrm{cm}^{2}$

$720 \; \textrm{cm}^{2}$

$1,440 \; \textrm{cm}^{2}$

Correct answer:

$720 \; \textrm{cm}^{2}$

Explanation:

The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting b=16,h=90 :

$A = \frac{1}{2} bh = \frac{1}{2} \cdot 16 \cdot 90= 720$

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Example Question #2 : Triangles

A triangle has base 18 inches and height 14 inches. What is its area?

Possible Answers:

$252 \; \textrm{in}^{2}$

$126 \; \textrm{in}^{2}$

$98 \; \textrm{in}^{2}$

$196 \; \textrm{in}^{2}$

$162 \; \textrm{in}^{2}$

Correct answer:

$126 \; \textrm{in}^{2}$

Explanation:

Use the area formula for a triangle, setting b=18,h=14 :

$A = \frac{1}{2} bh = \frac{1}{2} \cdot 18 \cdot14 = 126$

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Example Question #227 : Ssat Middle Level Quantitative (Math)

Triangle

What is the area of the above triangle?

Possible Answers:

$112\textrm{ in}^{2}$

$168\textrm{ in}^{2}$

$56\textrm{ in}^{2}$

$84\textrm{ in}^{2}$

$300\textrm{ in}^{2}$

Correct answer:

$84\textrm{ in}^{2}$

Explanation:

The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:

$\frac{1}{2} \cdot 7 \cdot 24 = 84$

That is, the area is 84 square inches.

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #221 : Ssat Middle Level Quantitative (Math)

Example Question #222 : Ssat Middle Level Quantitative (Math)

Example Question #223 : Ssat Middle Level Quantitative (Math)

Example Question #221 : Ssat Middle Level Quantitative (Math)

Example Question #222 : Ssat Middle Level Quantitative (Math)

Example Question #223 : Ssat Middle Level Quantitative (Math)

Example Question #224 : Ssat Middle Level Quantitative (Math)

Example Question #1 : Triangles

Example Question #2 : Triangles

Example Question #227 : Ssat Middle Level Quantitative (Math)

All SSAT Middle Level Math Resources

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