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ISEE Lower Level Math : Plane Geometry

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Example Questions

Example Question #1 : Quadrilaterals

Untitled_11

What is the perimeter of parallelogram ABCD?

Possible Answers:

$\displaystyle 8$

7.5 $\displaystyle 7.5$

Cannot be determined

$\displaystyle 15$

$\displaystyle 16$

Correct answer:

$\displaystyle 16$

Explanation:

The perimeter of a parallelogram is very easy to find. You just need to add up all the sides. However, you need to notice that the sides "across" from each other are equal on parallelograms. So, your figure could be redrawn:

Untitled_11

The perimeter of your figure is therefore:

$\displaystyle Perimeter = 5+5+3+3=16$

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

A parallelogram has a side length of 3 in $\displaystyle 3 in$. It also has a side length of 5 in $\displaystyle 5 in$. Calculate the perimeter.

Possible Answers:

16 in $\displaystyle 16 in$

10 in $\displaystyle 10 in$

9 in $\displaystyle 9 in$

8 in $\displaystyle 8 in$

15 in $\displaystyle 15 in$

Correct answer:

16 in $\displaystyle 16 in$

Explanation:

A parallelogram has four sides and its opposite sides are equal in length. Therefore, if it has one side length of 3 in $\displaystyle 3 in$, it also has another side length of of 3 in $\displaystyle 3 in$. Since we know one of its side lenghts is 5 in $\displaystyle 5 in$, then the remaining side is 5in $\displaystyle 5in$. We can add all 4 side lengths $\left ( 3 in, 3 in, 5 in, 5in\right )$ $\displaystyle \left ( 3 in, 3 in, 5 in, 5in\right )$to calculate the perimeter.

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Example Question #3 : Quadrilaterals

What is the perimeter of a parallelogram if the base is $\displaystyle 8$, the other side is $\displaystyle 2$, and the height is $\displaystyle 3$?

Possible Answers:

$\displaystyle 16$

$\displaystyle 10$

$\displaystyle 22$

$\displaystyle 24$

$\displaystyle 20$

Correct answer:

$\displaystyle 20$

Explanation:

The perimeter of a parallelogram is the sum of all four sides or the sum of two times each side length. The side lengths are $\displaystyle 2$ and $\displaystyle 8$ so the perimeter is $\displaystyle (2*8)+(2*2)=20$.

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Example Question #1 : Plane Geometry

Find the perimeter of the given parallelogram:

Capture

Possible Answers:

384 mi $\displaystyle 384 mi$

160 mi $\displaystyle 160 mi$

320 mi $\displaystyle 320 mi$

192 mi $\displaystyle 192 mi$

Correct answer:

320 mi $\displaystyle 320 mi$

Explanation:

Find the perimeter of the given parallelogram:

Capture

The perimeter of any shape can be found by adding up the lentghs of its sides.

In this case, we have four sides. 2 that are 16 miles long, and 2 that are 144 miles long.

Find perimeter as follows:

$\displaystyle P=2(16)+2(144)=32+288=320$

Making our answer 320 miles

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Example Question #21 : Geometry

Find the area of the parallelogram:

Question_11

Possible Answers:

$\displaystyle 16$

$\displaystyle 20$

$\displaystyle 40$

$\displaystyle 32$

Correct answer:

$\displaystyle 32$

Explanation:

$\displaystyle A=bh=(4)(8)=32$

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

Untitled_10

What is the area of the parallelogram ABCD?

Possible Answers:

$\displaystyle 60$

$\displaystyle 22$

$\displaystyle 15$

$\displaystyle 24$

$\displaystyle 12$

Correct answer:

$\displaystyle 24$

Explanation:

A parallelogram's area is found by multiplying its height by the base. The height of the parallelogram is not the side. It is the line that makes a right angle with the base. Therefore, the area of this parallelogram is:

$\displaystyle A=4*6=24$

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

Untitled_11

What is the area of parallelogram ABCD?

Possible Answers:

126 $\displaystyle 126$

357 $\displaystyle 357$

$\displaystyle 38$

252 $\displaystyle 252$

$\displaystyle 76$

Correct answer:

252 $\displaystyle 252$

Explanation:

$\displaystyle A=21*12=252$

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Example Question #8 : Quadrilaterals

A parallelogram measures 4 cm $\displaystyle 4 cm$ along its base and is 7 cm $\displaystyle 7 cm$ high. Calculate the area.

Possible Answers:

$26 cm^{2}$ $\displaystyle 26 cm^{2}$

$30 cm^{2}$ $\displaystyle 30 cm^{2}$

$22 cm^{2}$ $\displaystyle 22 cm^{2}$

$24 cm^{2}$ $\displaystyle 24 cm^{2}$

$28 cm^{2}$ $\displaystyle 28 cm^{2}$

Correct answer:

$28 cm^{2}$ $\displaystyle 28 cm^{2}$

Explanation:

The formula to calucate a parallelogram's area is:

$A = B \times H$ $\displaystyle A = B \times H$

You calculate the parallelogram's area by multiplying its base by its height. Therefore, $A = 4 cm \times 7 cm$ $\displaystyle A = 4 cm \times 7 cm$

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Example Question #1 : Quadrilaterals

A parallelogram measures 6 cm $\displaystyle 6 cm$ along its base and is 9 cm $\displaystyle 9 cm$ high. Calculate the area.

Possible Answers:

$48 cm^{2}$ $\displaystyle 48 cm^{2}$

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

$52 cm^{2}$ $\displaystyle 52 cm^{2}$

$54 cm^{2}$ $\displaystyle 54 cm^{2}$

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

Correct answer:

$54 cm^{2}$ $\displaystyle 54 cm^{2}$

Explanation:

The formula to calucate a parallelogram's area is:

$A = B\times H$ $\displaystyle A = B\times H$

You calculate the parallelogram's area by multiplying its base by its height. Therefore, $A = 6 cm \times 9 cm$ $\displaystyle A = 6 cm \times 9 cm$

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Example Question #23 : Geometry

Find the area of a parallelogram whose height is $\displaystyle 4$ and base is $\displaystyle 6$.

Possible Answers:

$\displaystyle 10$

$\displaystyle 12$

$\displaystyle 24$

$\displaystyle 20$

Correct answer:

$\displaystyle 24$

Explanation:

To solve, simply use the formula for the area of a parallelogram. Thus,

$\displaystyle A=Bh=6*4=24$

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ISEE Lower Level Math : Plane Geometry

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #1 : Quadrilaterals

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

Example Question #3 : Quadrilaterals

Example Question #1 : Plane Geometry

Example Question #21 : Geometry

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

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

Example Question #8 : Quadrilaterals

Example Question #1 : Quadrilaterals

Example Question #23 : Geometry

All ISEE Lower Level Math Resources

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