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ISEE Lower Level Math : Plane Geometry

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Example Questions

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

A triangle has a base that is 8 cm. and a height that is 12 cm. What is the area of this triangle?

Possible Answers:

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

$50\ cm^{2}$ $\displaystyle 50\ cm^{2}$

$36\ cm^{2}$ $\displaystyle 36\ cm^{2}$

$96\ cm^{2}$ $\displaystyle 96\ cm^{2}$

$60\ cm^{2}$ $\displaystyle 60\ cm^{2}$

Correct answer:

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

Explanation:

To find the area of the triangle, we need to plug in what we know (the base and the height) into the formula to find the area of the triangle:

$A=\frac{1}{2}bh$ $\displaystyle A=\frac{1}{2}bh$

$A=\frac{1}{2}*8*12$ $\displaystyle A=\frac{1}{2}*8*12$

We can know solve for $\displaystyle A$

$A=\frac{1}{2}*8*12$ $\displaystyle A=\frac{1}{2}*8*12$

A=4*12 $\displaystyle A=4*12$

$A=48cm.^{2}$ $\displaystyle A=48cm.^{2}$

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Example Question #4 : How To Find The Area Of A Triangle

Find the height of the triangle.

If the base of a triangle is 6mm $\displaystyle 6mm$ and the area is 12mm $\displaystyle 12mm$, what is the height of the triangle?

Possible Answers:

3mm $\displaystyle 3mm$

9mm $\displaystyle 9mm$

2mm $\displaystyle 2mm$

4mm $\displaystyle 4mm$

18mm $\displaystyle 18mm$

Correct answer:

4mm $\displaystyle 4mm$

Explanation:

Area of a triangle is

$\frac{1}{2}base\times height$ $\displaystyle \frac{1}{2}base\times height$

Set up the equation, then solve:

$\frac{1}{2}(6mm)\times h = 12mm$ $\displaystyle \frac{1}{2}(6mm)\times h = 12mm$

$(3mm)\times h=12mm$ $\displaystyle (3mm)\times h=12mm$

so h=4mm $\displaystyle h=4mm$

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Example Question #2 : How To Find The Area Of A Triangle

A triangle has a base of 7 and a height of 4. What is the area of the triangle?

Possible Answers:

$\displaystyle 14$

$\displaystyle 20$

None of these

$\displaystyle 8$

$\displaystyle 28$

Correct answer:

$\displaystyle 14$

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

$Area =\frac{base\cdot height}2{}$ $\displaystyle Area =\frac{base\cdot height}2{}$

Plugging in the appropriate values for this equation gives us:

$Area =\frac{7\cdot 4}2{}$ $\displaystyle Area =\frac{7\cdot 4}2{}$

This reduces to:

$Area =\frac{28}2{}=14$ $\displaystyle Area =\frac{28}2{}=14$

This is equal to 14, the correct answer.

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Example Question #3 : Triangles

A triangle has a base of 8 inches and a height of 4 inches. What is the area in square inches?

Possible Answers:

$16\ \text{in}^2$ $\displaystyle 16\ \text{in}^2$

$32\ \text{in}^2$ $\displaystyle 32\ \text{in}^2$

$14\ \text{in}^2$ $\displaystyle 14\ \text{in}^2$

$12\ \text{in}^2$ $\displaystyle 12\ \text{in}^2$

$8\ \text{in}^2$ $\displaystyle 8\ \text{in}^2$

Correct answer:

$16\ \text{in}^2$ $\displaystyle 16\ \text{in}^2$

Explanation:

The area of a triangle can be calculated using this formula:

$Area=\frac{base\cdot height}{2}$ $\displaystyle Area=\frac{base\cdot height}{2}$

When inputting the base and height information, the equation looks like this:

$Area=\frac{8\cdot 4}{2}$ $\displaystyle Area=\frac{8\cdot 4}{2}$

$Area=\frac{32}{2}$ $\displaystyle Area=\frac{32}{2}$

Area=16 $\displaystyle Area=16$

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Example Question #282 : Plane Geometry

The area of a triangle is 12 square inches. It has a height of 4 inches. What is the triangle's base, in inches?

Possible Answers:

$\displaystyle 4$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 2$

$\displaystyle 5$

Correct answer:

$\displaystyle 6$

Explanation:

The area of a triangle is:

$A = \frac{1}{2}b\times h$ $\displaystyle A = \frac{1}{2}b\times h$

Given that the area is 12 and the base is 4, this gives us:

$12= \frac{1}{2}(4)\times h$ $\displaystyle 12= \frac{1}{2}(4)\times h$

This reduces to:

$12= 2\times h$ $\displaystyle 12= 2\times h$

6= h $\displaystyle 6= h$

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Example Question #4 : Triangles

If a triangle has a base of 1 foot, and a height of half a foot, what is the area in square inches?

Possible Answers:

$0.25\ \text{in}^2$ $\displaystyle 0.25\ \text{in}^2$

$72\ \text{in}^2$ $\displaystyle 72\ \text{in}^2$

$36\ \text{in}^2$ $\displaystyle 36\ \text{in}^2$

$42\ \text{in}^2$ $\displaystyle 42\ \text{in}^2$

$0.5\ \text{in}^2$ $\displaystyle 0.5\ \text{in}^2$

Correct answer:

$36\ \text{in}^2$ $\displaystyle 36\ \text{in}^2$

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

$Area =\frac{base\cdot height}{2}$ $\displaystyle Area =\frac{base\cdot height}{2}$

Since we are looking for the area in inches, we must convert the base and height to inches, from feet.

$1\text{ft}=12\text{in}=base$ $\displaystyle 1\text{ft}=12\text{in}=base$

$\frac{1}{2}\text{ft}=6\text{in}=height$ $\displaystyle \frac{1}{2}\text{ft}=6\text{in}=height$

This gives us a base of 6 inches and a height of 12 inches. Plug these values into the area equation and solve.

$Area =\frac{6\cdot 12}{2}$ $\displaystyle Area =\frac{6\cdot 12}{2}$

$Area =\frac{72}{2}$ $\displaystyle Area =\frac{72}{2}$

Area=36 $\displaystyle Area=36$

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Example Question #11 : How To Find The Area Of A Triangle

What is the area of a triangle for which the base is 9 inches and the height is 12 inches?

Possible Answers:

$48\ \text{in}^2$ $\displaystyle 48\ \text{in}^2$

$46\ \text{in}^2$ $\displaystyle 46\ \text{in}^2$

$42\ \text{in}^2$ $\displaystyle 42\ \text{in}^2$

$54\ \text{in}^2$ $\displaystyle 54\ \text{in}^2$

$52\ \text{in}^2$ $\displaystyle 52\ \text{in}^2$

Correct answer:

$54\ \text{in}^2$ $\displaystyle 54\ \text{in}^2$

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

$Area =\frac{base\cdot height}{2}$ $\displaystyle Area =\frac{base\cdot height}{2}$

Given that the base is 9 inches and the height is 12 inches, plugging these numbers into the equation gives us the following:

$Area =\frac{9\cdot 12}{2}$ $\displaystyle Area =\frac{9\cdot 12}{2}$

$Area = \frac{108}{2}$ $\displaystyle Area = \frac{108}{2}$

Area=54 $\displaystyle Area=54$

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Example Question #11 : How To Find The Area Of A Triangle

If a triangle has a height of 2 inches and a base that is 3 times as long, what is the area?

Possible Answers:

$\displaystyle 3$

$\displaystyle 4$

$\displaystyle 12$

$\displaystyle 6$

Correct answer:

$\displaystyle 6$

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

Given that the height is 2 inches, and the base is 3 times that of the height, the base is 6 inches.

$Area =\frac{base\cdot height}{2}$ $\displaystyle Area =\frac{base\cdot height}{2}$

$Area =\frac{6\cdot 2}2{}$ $\displaystyle Area =\frac{6\cdot 2}2{}$

Area =6 $\displaystyle Area =6$

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Example Question #12 : How To Find The Area Of A Triangle

If the area of a triangle is 15 feet and the height is 5 feet, what is the length of the base?

Possible Answers:

$\displaystyle 3$

$\displaystyle 4$

$\displaystyle 5$

$\displaystyle 6$

Correct answer:

$\displaystyle 6$

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

$Area =\frac{base\cdot height}{2}$ $\displaystyle Area =\frac{base\cdot height}{2}$

$15=\frac{5\cdot base}{2}$ $\displaystyle 15=\frac{5\cdot base}{2}$

Each side of the equation should be multiplied by 2.

$30=5\cdot base$ $\displaystyle 30=5\cdot base$

Each side should be divided by 5.

Therefore, the base has a value of 6.

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Example Question #11 : How To Find The Area Of A Triangle

A triangle has a height of 6 inches and a base of 3 inches. What is the area, in square inches?

Possible Answers:

$11\ \text{in}^2$ $\displaystyle 11\ \text{in}^2$

$12\ \text{in}^2$ $\displaystyle 12\ \text{in}^2$

$18\ \text{in}^2$ $\displaystyle 18\ \text{in}^2$

$9\ \text{in}^2$ $\displaystyle 9\ \text{in}^2$

$10\ \text{in}^2$ $\displaystyle 10\ \text{in}^2$

Correct answer:

$9\ \text{in}^2$ $\displaystyle 9\ \text{in}^2$

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by 2.

$\text{Area} =\frac{\text{base}\times\text{height}}{2}$ $\displaystyle \text{Area} =\frac{\text{base}\times\text{height}}{2}$

Here, the base is 3 inches and the height is 6 inches. When plugging this information into the formula, we get:

$Area =\frac{3\times 6}{2}$ $\displaystyle Area =\frac{3\times 6}{2}$

$Area=\frac{18}{2}$ $\displaystyle Area=\frac{18}{2}$

This fraction reduces to 9, the correct answer.

$\frac{18}{2}=\frac{18\div2}{2\div2}=\frac{9}{1}=9$ $\displaystyle \frac{18}{2}=\frac{18\div2}{2\div2}=\frac{9}{1}=9$

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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 : How To Find The Area Of A Triangle

Example Question #4 : How To Find The Area Of A Triangle

Example Question #2 : How To Find The Area Of A Triangle

Example Question #3 : Triangles

Example Question #282 : Plane Geometry

Example Question #4 : Triangles

Example Question #11 : How To Find The Area Of A Triangle

Example Question #11 : How To Find The Area Of A Triangle

Example Question #12 : How To Find The Area Of A Triangle

Example Question #11 : How To Find The Area Of A Triangle

All ISEE Lower Level Math Resources

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