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ISEE Lower Level Math : How to find the area of a triangle

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Example Questions

Example Question #41 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 7in and a height that is two times the base.

Possible Answers:

$49\text{in}^2$ $\displaystyle 49\text{in}^2$

$56\text{in}^2$ $\displaystyle 56\text{in}^2$

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

$98\text{in}^2$ $\displaystyle 98\text{in}^2$

$78\text{in}^2$ $\displaystyle 78\text{in}^2$

Correct answer:

$49\text{in}^2$ $\displaystyle 49\text{in}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

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

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 7in. We also know the height is two times the base. Therefore, the height is 14in.

Knowing this, we can substitute into the formula. We get

$A = \frac{1}{2} \cdot 7\text{in} \cdot 14\text{in}$ $\displaystyle A = \frac{1}{2} \cdot 7\text{in} \cdot 14\text{in}$

$A = 7\text{in} \cdot 7\text{in}$ $\displaystyle A = 7\text{in} \cdot 7\text{in}$

$A = 49\text{in}^2$ $\displaystyle A = 49\text{in}^2$

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Example Question #42 : How To Find The Area Of A Triangle

Find the area of a triangle with the following measurements:

height: 5in
base: 6in

Possible Answers:

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

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

$17\text{in}^2$ $\displaystyle 17\text{in}^2$

$30\text{in}^2$ $\displaystyle 30\text{in}^2$

$15\text{in}^2$ $\displaystyle 15\text{in}^2$

Correct answer:

$15\text{in}^2$ $\displaystyle 15\text{in}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

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

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 6in. We also know the height of the triangle is 5in. So, we get

$A = \frac{1}{2} \cdot 6\text{in} \cdot 5\text{in}$ $\displaystyle A = \frac{1}{2} \cdot 6\text{in} \cdot 5\text{in}$

$A = 3\text{in} \cdot 5\text{in}$ $\displaystyle A = 3\text{in} \cdot 5\text{in}$

$A = 15\text{in}^2$ $\displaystyle A = 15\text{in}^2$

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Example Question #43 : How To Find The Area Of A Triangle

Use the following triangle to answer the question:

Triangle5

If the triangle has a height of $9\textup{ ft}$ $\displaystyle 9\textup{ ft}$ , find the area.

Possible Answers:

$17\textup{ ft}^2$ $\displaystyle 17\textup{ ft}^2$

$26\textup{ ft}^2$ $\displaystyle 26\textup{ ft}^2$

$21\textup{ ft}^2$ $\displaystyle 21\textup{ ft}^2$

$20\textup{ ft}^2$ $\displaystyle 20\textup{ ft}^2$

$18\textup{ ft}^2$ $\displaystyle 18\textup{ ft}^2$

Correct answer:

$18\textup{ ft}^2$ $\displaystyle 18\textup{ ft}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$ $\displaystyle \text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, given the triangle

Triangle5

we can see the base is 4ft. We also know it has a height of 9ft.

Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 4\text{ft} \cdot 9\text{ft}$ $\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 4\text{ft} \cdot 9\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 36\text{ft}^2$ $\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 36\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{36\text{ft}^2}{1}$ $\displaystyle \text{area of triangle} = \frac{1}{2} \cdot \frac{36\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 36\text{ft}^2}{2 \cdot 1}$ $\displaystyle \text{area of triangle} = \frac{1 \cdot 36\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{36\text{ft}^2}{2}$ $\displaystyle \text{area of triangle} = \frac{36\text{ft}^2}{2}$

$\text{area of triangle} = 18\text{ft}^2$ $\displaystyle \text{area of triangle} = 18\text{ft}^2$

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ISEE Lower Level Math : How to find the area of a triangle

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #41 : How To Find The Area Of A Triangle

Example Question #42 : How To Find The Area Of A Triangle

Example Question #43 : How To Find The Area Of A Triangle

All ISEE Lower Level Math Resources

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