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ISEE Lower Level Math : Triangles

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Example Questions

Example Question #1 : Triangles

The base of triangle ABC is $\dpi{100} 6\ cm$ $\displaystyle \dpi{100} 6\ cm$, it's height $\dpi{100} 12\ cm$ $\displaystyle \dpi{100} 12\ cm$. What is the triangle's area?

Possible Answers:

$\dpi{100} 18\ cm^{2}$ $\displaystyle \dpi{100} 18\ cm^{2}$

$\dpi{100} 30\ cm^{2}$ $\displaystyle \dpi{100} 30\ cm^{2}$

$\dpi{100} 72\ cm^{2}$ $\displaystyle \dpi{100} 72\ cm^{2}$

$\dpi{100} 36\ cm^{2}$ $\displaystyle \dpi{100} 36\ cm^{2}$

Correct answer:

$\dpi{100} 36\ cm^{2}$ $\displaystyle \dpi{100} 36\ cm^{2}$

Explanation:

$\dpi{100} Area=\frac{1}{2}\ base\times height$ $\displaystyle \dpi{100} Area=\frac{1}{2}\ base\times height$

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Example Question #292 : Geometry

What is the area of a triangle that has a base of $14\ cm$ $\displaystyle 14\ cm$ and a height of $5\ cm.$ $\displaystyle 5\ cm.$

Possible Answers:

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

$38 cm^{2}$ $\displaystyle 38 cm^{2}$

$35 cm^{2}$ $\displaystyle 35 cm^{2}$

$42 cm^{2}$ $\displaystyle 42 cm^{2}$

$19 cm^{2 }$ $\displaystyle 19 cm^{2 }$

Correct answer:

$35 cm^{2}$ $\displaystyle 35 cm^{2}$

Explanation:

In order to find the area of a triangle, we must use the formula

$\frac{1}{2}\left ( b\cdot h \right )$ $\displaystyle \frac{1}{2}\left ( b\cdot h \right )$

So the first thing we must do is multiply the base and height.

$14cm\cdot 5 cm = 70 cm^{2}$ $\displaystyle 14cm\cdot 5 cm = 70 cm^{2}$

The next thing we must do is find $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ of $\displaystyle 70$ through multiplication.

$\small \frac{1}{2}$ $\displaystyle \small \frac{1}{2}$ $\cdot 70 cm^{2}=35 cm^{2}$ $\displaystyle \cdot 70 cm^{2}=35 cm^{2}$

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Example Question #1 : Triangles

Find the area of the triangle:

Question_12

Possible Answers:

$\displaystyle 56$

$\displaystyle 35$

$\displaystyle 84$

$\displaystyle 80$

Correct answer:

$\displaystyle 35$

Explanation:

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

$A=\frac{1}{2}(10)(7)$ $\displaystyle A=\frac{1}{2}(10)(7)$

$\displaystyle A=(5)(7)=35$

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Example Question #3 : Triangles

A triangle has an area of 36 in.². if its base is 6 in., what is its height?

Possible Answers:

$3\ in$ $\displaystyle 3\ in$

$36\ in$ $\displaystyle 36\ in$

$12\ in$ $\displaystyle 12\ in$

$24\ in$ $\displaystyle 24\ in$

$6\ in$ $\displaystyle 6\ in$

Correct answer:

$12\ in$ $\displaystyle 12\ in$

Explanation:

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

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

$36=\frac{1}{2}6h$ $\displaystyle 36=\frac{1}{2}6h$

Now that you plugged in the area and the base into the formula to find the area of a triangle, you can solve for the height:

Multiply both sides by 2 (the reciprocal of 1/2) to get rid of the fraction

$2*36=\frac{1}{2}6h*2$ $\displaystyle 2*36=\frac{1}{2}6h*2$

72=6h $\displaystyle 72=6h$

Divide both sides by 6 to find the height

$\frac{72}{6}=\frac{6}{6}h$ $\displaystyle \frac{72}{6}=\frac{6}{6}h$

12=1*h $\displaystyle 12=1*h$ Remember that 1*h $\displaystyle 1*h$ is the same as $\displaystyle h$

12=h $\displaystyle 12=h$

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Example Question #293 : Geometry

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:

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

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

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

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

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

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 #2 : 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:

4mm $\displaystyle 4mm$

18mm $\displaystyle 18mm$

3mm $\displaystyle 3mm$

2mm $\displaystyle 2mm$

9mm $\displaystyle 9mm$

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 #1 : 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:

$\displaystyle 8$

$\displaystyle 20$

None of these

$\displaystyle 28$

$\displaystyle 14$

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:

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

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

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

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

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

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 #1231 : Isee Lower Level (Grades 5 6) Mathematics Achievement

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:

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

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

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

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

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

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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ISEE Lower Level Math : Triangles

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #1 : Triangles

Example Question #292 : Geometry

Example Question #1 : Triangles

Example Question #3 : Triangles

Example Question #293 : Geometry

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

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

Example Question #3 : Triangles

Example Question #282 : Plane Geometry

Example Question #1231 : Isee Lower Level (Grades 5 6) Mathematics Achievement

All ISEE Lower Level Math Resources

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