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SSAT Middle Level Math : Plane Geometry

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Example Questions

Example Question #171 : Geometry

A parallelogram has a base of length $30\:cm$ $\displaystyle 30\:cm$, a height of length $15\:cm$ $\displaystyle 15\:cm$, and a side of length $13\:cm$ $\displaystyle 13\:cm$. What is the area of the parallelogram?

Possible Answers:

$450\:cm^{2}$ $\displaystyle 450\:cm^{2}$

$300\:cm^{2}$ $\displaystyle 300\:cm^{2}$

$45\:cm^{2}$ $\displaystyle 45\:cm^{2}$

$390\:cm^{2}$ $\displaystyle 390\:cm^{2}$

$195\:cm^{2}$ $\displaystyle 195\:cm^{2}$

Correct answer:

$450\:cm^{2}$ $\displaystyle 450\:cm^{2}$

Explanation:

Given base (b) $\displaystyle (b)$ and height (h) $\displaystyle (h)$, $A=b\times h$ $\displaystyle A=b\times h$.

Substituting the values from our question:

$A= 30\:cm\times15\:cm$ $\displaystyle A= 30\:cm\times15\:cm$

$A=450\:cm^{2}$ $\displaystyle A=450\:cm^{2}$

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Example Question #131 : Plane Geometry

Find the area of a parallelogram with a height of $9\:cm$ $\displaystyle 9\:cm$, a base of $8\:cm$ $\displaystyle 8\:cm$, and a side length of $7\:cm$ $\displaystyle 7\:cm$.

Possible Answers:

$56\:cm^{2}$ $\displaystyle 56\:cm^{2}$

$63\:cm^{2}$ $\displaystyle 63\:cm^{2}$

$72\:cm^{2}$ $\displaystyle 72\:cm^{2}$

$72\:cm$ $\displaystyle 72\:cm$

$63\:cm$ $\displaystyle 63\:cm$

Correct answer:

$72\:cm^{2}$ $\displaystyle 72\:cm^{2}$

Explanation:

The area $\displaystyle A$ of a parallelogram with height $\displaystyle h$ and base $\displaystyle b$ can be found with the equation A=bh $\displaystyle A=bh$. Consequently:

A=bh $\displaystyle A=bh$

$A=(9\:cm)(8\:cm)$ $\displaystyle A=(9\:cm)(8\:cm)$

$A=72\:cm^{2}$ $\displaystyle A=72\:cm^{2}$

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Example Question #6 : Parallelograms

Find the area of a parallelogram with a height of $12\:cm$ $\displaystyle 12\:cm$, base of $11\:cm$ $\displaystyle 11\:cm$, and a side length of $7\:cm$ $\displaystyle 7\:cm$.

Possible Answers:

$132\:cm$ $\displaystyle 132\:cm$

$77\:cm$ $\displaystyle 77\:cm$

$77\:cm^{2}$ $\displaystyle 77\:cm^{2}$

$132\:cm^{2}$ $\displaystyle 132\:cm^{2}$

$84\:cm^{2}$ $\displaystyle 84\:cm^{2}$

Correct answer:

$132\:cm^{2}$ $\displaystyle 132\:cm^{2}$

Explanation:

The area $\displaystyle A$ of a parallelogram with height $\displaystyle h$ and base $\displaystyle b$ can be found with the equation A=bh $\displaystyle A=bh$. Consequently:

A=bh $\displaystyle A=bh$

$A=(12\:cm)(11\:cm)$ $\displaystyle A=(12\:cm)(11\:cm)$

$A=132\:cm^{2}$ $\displaystyle A=132\:cm^{2}$

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Example Question #2 : Geometry

Find the area of the following parallelogram:

Note: The formula for the area of a parallelogram is $A=b\times h$ $\displaystyle A=b\times h$.

Possible Answers:

$60\: in^2$ $\displaystyle 60\: in^2$

$32\: in^2$ $\displaystyle 32\: in^2$

$50\: in^2$ $\displaystyle 50\: in^2$

$30\: in^2$ $\displaystyle 30\: in^2$

Correct answer:

$50\: in^2$ $\displaystyle 50\: in^2$

Explanation:

The base of the parallelogram is 10, while the height is 5.

$A=b\times h$ $\displaystyle A=b\times h$

$A=10\times5=50\: in^2$ $\displaystyle A=10\times5=50\: in^2$

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Example Question #3 : Geometry

Find the area:

Question_5

Possible Answers:

$\displaystyle 15$

$\small 32$ $\displaystyle \small 32$

$\small 24$ $\displaystyle \small 24$

$\small 12$ $\displaystyle \small 12$

$\small 16$ $\displaystyle \small 16$

Correct answer:

$\small 24$ $\displaystyle \small 24$

Explanation:

The area of a parallelogram can be determined using the following equation:

$\small A=bh$ $\displaystyle \small A=bh$

Therefore,

$\small A=8\times3=24$ $\displaystyle \small A=8\times3=24$

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Example Question #133 : Plane Geometry

Parallelogram

Find the area of the given parallelogram if $\displaystyle h=5, b=8, c=6$ .

Possible Answers:

$\displaystyle 40$

$\displaystyle 38$

$\displaystyle 30$

$\displaystyle 28$

$\displaystyle 48$

Correct answer:

$\displaystyle 40$

Explanation:

In order to find the area of a parallelogram, we need to find the product of the base length and height.

$\displaystyle A=(b)(h)=(8)(5)=40$

Notice that only two of the given values were needed to slove this problem.

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

Parallelogram

Find the perimeter of the given parallelogram if $\displaystyle h=3, b=5, c=4$

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter, we find the sum of the OUTER sides:

Parallelogram_labeled

$\displaystyle 5+5+4+4=18$

Notice that we didn't use the height in our calculation.

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

Parallelogram

Find the perimeter of the given parallelogram if $\displaystyle h=6, c=8, b=10$

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter of the parallelogram, we must add the OUTER edges:

Parallelogram_labeled

$\displaystyle 10+10+8+8=36$

Notice that we didn't use height in our calculation.

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

Parallelogram

Find the perimeter of the given parallelogram if $\displaystyle h=5, b=10, c=8$

Possible Answers:

Correct answer:

Explanation:

In order to find the perimeter, we need to find the sum of the outer edges:

Parallelogram_labeled

$\displaystyle 10+10+8=8=36$

Notice that we didn't use height in our calculation.

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

Find the area of a parallelogram with base length $8\:cm$ $\displaystyle 8\:cm$ and side length $5\:cm$ $\displaystyle 5\:cm$.

Possible Answers:

$20\:cm$ $\displaystyle 20\:cm$

$20\:cm^{2}$ $\displaystyle 20\:cm^{2}$

$40\:cm$ $\displaystyle 40\:cm$

$40\:cm^{2}$ $\displaystyle 40\:cm^{2}$

Not enough information provided

Correct answer:

Not enough information provided

Explanation:

The area $\displaystyle A$ of a parallelogram with height $\displaystyle h$ and base $\displaystyle b$ can be found with the equation A=bh $\displaystyle A=bh$. However, while we have been given the length of the base and of another side of the parallelogram, we still do not know the length of the base. Therefore, we do not have enough information to find the area.

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SSAT Middle Level Math : Plane Geometry

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #171 : Geometry

Example Question #131 : Plane Geometry

Example Question #6 : Parallelograms

Example Question #2 : Geometry

Example Question #3 : Geometry

Example Question #133 : Plane Geometry

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

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

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

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

All SSAT Middle Level Math Resources

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