# 10.4: Unknown Dimensions of Triangles

**At Grade**Created by: CK-12

**Practice**Unknown Dimensions of Triangles

Remember Marie, who had parallelograms in her quilt square? Well, Marie also had triangles. Take a look.

Jillian enjoyed working on her quilt square next to Marie. Marie was very patient and also offered Jillian a lot of support. Marie's quilt square was made up of parallelograms and also triangles.

One of the triangles had an area of 8 square inches with a base of 4 inches.

Jillian is wondering about the height of the triangle.

Do you know how to figure it out?

**This Concept is about figuring out missing dimensions. You will know how to solve this problem by the end of it.**

### Guidance

What happens if you have been given the area of a triangle and one other dimension?

When this happens, you have to be a detective and figure out the missing dimension. For instance, if you have been given the area and the base of a triangle, then you have to figure out the height. If you have been given the area and the height then you have to figure out the base.

**You have to be a detective!**

Now let’s use the formula for finding the area of a triangle to solve this problem. Remember, you will need your detective skills.

A triangle has an area of 36 square inches and a height of 6 inches. What is the measure of the base?

**To figure this out, we start by looking at the formula for finding the area of a triangle.**

\begin{align*}A = \frac{1}{2}bh\end{align*}

Next, we fill in the given information.

\begin{align*}36 = \frac{1}{2}(6)b\end{align*}

To solve this problem, we need to first multiply one-half by six.

\begin{align*}36 = 3b\end{align*}

Next, we need to solve for the base. We do this by thinking about what number times three is equal to thirty-six. You could also think of it as dividing thirty-six by 3.

Our answer is 12. The base of this triangle is 12 inches.

Try a few of these on your own.

#### Example A

A triangle has an area of 42 sq. ft. If the base is 12 feet, what is the measure of the height?

**Solution: 7 feet**

#### Example B

A triangle has an area of 16 sq. cm. If the height of the triangle is 4 cm, what is the measure of the base?

**Solution: 8 cm**

#### Example C

A triangle has an area of 40 sq. meters and a base of 10. What is the height?

**Solution: 8 meters**

Now let's go back to the dilemma with Jillian and the quilt square.

Jillian enjoyed working on her quilt square next to Marie. Marie was very patient and also offered Jillian a lot of support. Marie's quilt square was made up of parallelograms and also triangles.

One of the triangles had an area of 8 square inches with a base of 4 inches.

Jillian is wondering about the height of the triangle.

Now you should know how to figure this out. Let's go through the steps.

**To figure this out, we start by looking at the formula for finding the area of a triangle.**

\begin{align*}A = \frac{1}{2}bh\end{align*}

Next, we fill in the given information.

\begin{align*}8 = \frac{1}{2}(4)h\end{align*}

To solve this problem, we need to first multiply one-half by 4.

\begin{align*}8 = 2h\end{align*}

Next, we need to solve for the base. We do this by thinking about what number times two is equal to eight. You could also think of it as dividing eight by 2.

Our answer is 4 . The height of this triangle is 4 inches.

**This is our answer.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Triangle
- a polygon with three sides.

- Parallelogram
- a four sided figure with opposite sides congruent and parallel.

- Rectangle
- a parallelogram with opposite sides congruent and parallel and with four right angles.

- Square
- a parallelogram with four congruent, parallel sides and four congruent right angles.

### Guided Practice

Here is one for you to try on your own.

The area of the triangle is 48 square feet. The base of the triangle is 12 feet. What is the height?

**Answer**

Let's go through the steps to figure out this problem.

To figure this out, we start by looking at the formula for finding the area of a triangle.

\begin{align*}A = \frac{1}{2}bh\end{align*}

Next, we fill in the given information.

\begin{align*}48 = \frac{1}{2}(12)h\end{align*}

To solve this problem, we need to first multiply one-half by 12.

\begin{align*}48 = 6h\end{align*}

Next, we need to solve for the base. We do this by thinking about what number times six is equal to forty- eight. You could also think of it as dividing forty - eight by 6.

Our answer is 8 . The height of this triangle is 8 feet.

**This is our answer.**

### Video Review

Here is a video for review.

James Sousa, Example of the Area of a Triangle

### Practice

Directions: Find the missing dimension of the triangle given an area and a base or height.

1. Area = 15 sq. in, Base = 10 in, what is the height?

2. Area = 40 sq. in, Base = 20 in, what is the height?

3. Area = 24 sq. ft, Base = 8 ft, what is the height?

4. Area = 16 sq. m, Base = 8 m, what is the height?

5. Area = 25 sq. in, height = 5 in, what is the base?

6. Area = 36 sq. ft, Height = 6 ft, what is the base?

7. Area = 54 sq. cm, Height = 9 cm, what is the base?

8. Area = 80 sq. meters, Base = 16 meters, what is the height?

9. Area = 75 sq. meters, Base = 10 meters, what is the height?

10. Area = 90 sq. meters, Base = 30 meters, what is the height?

11. Area = 180 sq. meters, Base = 10 meters, what is the height?

12. Area = 90 sq. meters, Base = 15 meters, what is the height?

13. Area = 120 sq. meters, Base = 60 meters, what is the height?

14. Area = 150 sq. meters, Base = 50 meters, what is the height?

15. Area = 280 sq. meters, Base = 140 meters, what is the height?

### Image Attributions

Here you'll find the unknown dimensions of triangles given the area and another dimension.