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

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Example Questions

Example Question #53 : Triangles

Your neighbor is building a sandbox out of two by fours. The sandbox will be in the shape of a right triangle, with the legs being 12 feet and 16 feet. What will the area of the sandbox be?

Possible Answers:

192ft^2

108ft^2

96 ft^2

48ft^2

Correct answer:

96 ft^2

Explanation:

Your neighbor is building a sandbox out of two by fours. The sandbox will be in the shape of a right triangle, with the legs being 12 feet and 16 feet. What will the area of the sandbox be?

The are of a triangle is found as follows:

$A_{triangle}=\frac{1}{2}b*h$

Where b is the length of the base and h is the length of the height.

We are told two lengths of our triangle, and because it is a right triangle, we can use them as base and height. Note that it doesn't really matter which one is which.

$A=\frac{1}{2}*12ft*16ft=6ft*16ft=96ft^2$

Because this is an area question, our units must be squared.

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Example Question #51 : Triangles

Find the area of a triangle with a base of length 6 feet and a height that is two times the base.

Possible Answers:

$72\text{ft}^2$

$36\text{ft}^2$

$36\text{ft}$

$12\text{ft}^2$

$72\text{ft}$

Correct answer:

$36\text{ft}^2$

Explanation:

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

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

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

Now, we know the base has a length of 6 feet. We also know the height is two times the base. Therefore, the height is 12 feet. Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{ft} \cdot 12\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 72\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{72\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 72\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{72\text{ft}^2}{2}$

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

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Example Question #56 : Triangles

Find the area of a triangle with a base of 7cm and a height of 12cm.

Possible Answers:

$84\text{cm}$

$42\text{cm}^2$

$84\text{cm}^2$

$48\text{cm}^2$

$42\text{cm}$

Correct answer:

$42\text{cm}^2$

Explanation:

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

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

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

We know the base is 7cm and the height is 12cm. Knowing this, we will substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 7\text{cm} \cdot 12\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 84\text{cm}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{84\text{cm}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 84\text{cm}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{84\text{cm}^2}{2}$

$\text{area of triangle} = 42\text{cm}^2$

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Example Question #21 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 6 feet and a height that is twice the base.

Possible Answers:

$12\text{ft}^2$

$42\text{ft}^2$

$18\text{ft}^2$

$36\text{ft}^2$

$72\text{ft}^2$

Correct answer:

$36\text{ft}^2$

Explanation:

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

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

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

Now, we know the base is 6ft. We also know the height is twice (or two times) the base. Therefore, the height is 12ft.

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

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{ft} \cdot 12\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 72\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{72\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 72\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{72\text{ft}^2}{2}$

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

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Example Question #58 : Triangles

Find the area of a triangle with a base of 6cm and a height of 18cm.

Possible Answers:

$54\text{cm}$

$108\text{cm}$

$54\text{cm}^2$

$42\text{cm}^2$

$108\text{cm}^2$

Correct answer:

$54\text{cm}^2$

Explanation:

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

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

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

Now, we know the base of the triangle is 6cm. We also know the height of the triangle is 18cm.

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

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{cm} \cdot 18\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 108\text{cm}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{108\text{cm}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 108\text{cm}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{108\text{cm}^2}{2}$

$\text{area of triangle} = 54\text{cm}^2$

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Example Question #22 : How To Find The Area Of A Triangle

Use the following image to answer the question:

Triangle6

Find the area of the triangle if it has a height of 11 feet.

Possible Answers:

$39\text{ft}^2$

$72\text{ft}^2$

$66\text{ft}^2$

$33\text{ft}^2$

$60\text{ft}^2$

Correct answer:

$33\text{ft}^2$

Explanation:

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

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

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

Now, let's look at the triangle.

Triangle6

We can see it has a base of 6 feet. We also know it has a height of 11 feet.

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

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{ft} \cdot 11\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 66\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{66\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 66\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{66\text{ft}^2}{2}$

$\text{area of triangle} = 33\text{ft}^2$

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Example Question #60 : Triangles

Find the area of a triangle with a height of 12 feet and a base that is half the height.

Possible Answers:

$72\text{ft}^2$

$18\text{ft}^2$

$36\text{ft}^2$

$24\text{ft}^2$

$6\text{ft}^2$

Correct answer:

$36\text{ft}^2$

Explanation:

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

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

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

Now, we know the height of the triangle is 12 feet. We also know the base is half the height. Therefore, the base is 6 feet.

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

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{ft} \cdot 12\text{ft}$

$\text{area of triangle} = 3\text{ft} \cdot 12\text{ft}$

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

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Example Question #61 : Geometry

Find the area of a triangle with a base of 17in and a height of 12in.

Possible Answers:

$121\text{in}^2$

$144\text{in}^2$

$29\text{in}^2$

$41\text{in}^2$

$102\text{in}^2$

Correct answer:

$102\text{in}^2$

Explanation:

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

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

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

Now, we know the base of the triangle is 17in. We also know the height of the triangle is 12in.

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

$\text{area of triangle} = \frac{1}{2} \cdot 17\text{in} \cdot 12\text{in}$

$\text{area of triangle} = 17\text{in} \cdot 6\text{in}$

$\text{area of triangle} = 102\text{in}^2$

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Example Question #21 : How To Find The Area Of A Triangle

Find the area of a triangle with the following measurements:

Height: 13in
Base: 8in

Possible Answers:

$96\text{in}^2$

$48\text{in}^2$

$36\text{in}^2$

$104\text{in}^2$

$52\text{in}^2$

Correct answer:

$52\text{in}^2$

Explanation:

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

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

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

Now, we know the base is 8in. We also know the height is 13in. We can substitute into the formula. We get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 13\text{in}$

$A = 4\text{in} \cdot 13\text{in}$

$A = 52\text{in}^2$

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Example Question #21 : How To Find The Area Of A Triangle

Find the area of a triangle with the following measurements:

base = 8in
height = 7in

Possible Answers:

$36\text{in}^2$

$28\text{in}^2$

$15\text{in}^2$

$24\text{in}^2$

$56\text{in}^2$

Correct answer:

$28\text{in}^2$

Explanation:

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

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

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

Now, we know the base is 8in and the height is 7in. Knowing this, we can substitute into the formula. So, we get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 7\text{in}$

$A = 4\text{in} \cdot 7\text{in}$

$A = 28\text{in}^2$

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All ISEE Middle Level Math Resources

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

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #53 : Triangles

Example Question #51 : Triangles

Example Question #56 : Triangles

Example Question #21 : How To Find The Area Of A Triangle

Example Question #58 : Triangles

Example Question #22 : How To Find The Area Of A Triangle

Example Question #60 : Triangles

Example Question #61 : Geometry

Example Question #21 : How To Find The Area Of A Triangle

Example Question #21 : How To Find The Area Of A Triangle

All ISEE Middle Level Math Resources

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