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Area of a Triangle
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A triangle is just half of a rectangle, to find the area of a triangle, you find the area of the rectangle the triangle fits inside and divide it by 2. Here are some vocabulary words to help with the lesson.

• Base: The width of a triangle
• Perpendicular: 2 lines that touch at a 90 degree angle. (See the information box on right angles within the lesson on the perimeter of a rectangle.)
• Adjacent sides: Sides of a shape that meet at a corner
Area of a Triangle

$$\displaystyle \text{Area of Triangle} = \frac{1}{2}\text{base} \times \text{height} = \frac{1}{2}{\text{bh}}$$

Remember that the base and the height have to be perpendicular to each other. In this course, we will provide the base and height values.

Practice Problems

1. A triangle has a base of 10 mm and a height of 12 mm. Use the formula for the area of a triangle to determine the area of this triangle. (
Solution
Solution:
$$60 \text{ mm}^{2}$$
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2. A triangle has a base of 5 inches and a height of 7 inches. Use the formula for the area of a triangle to determine the area of this triangle. Round to the nearest tenth. (
Solution
Solution:
$$17.5 \text{ in}^{2}$$
Details:
We want to find the area of a triangle with a base of 5 in and a height of 7 in.

To find the area of a triangle, it helps to look at a rectangle with sides that are equal to the base and the height that is cut in half in the following way:

As you can see, the area of the triangle is half of the area of the rectangle with the same length and width. To find the area of a rectangle we multiply the $$\color{blue} \text{width}$$ times the $$\color{red} \text{length}$$. To find the area of the triangle, we multiply the width times the length then divide it by two.

$${\text{A}}=\dfrac{1}{2}({\text{b}}\times {\text{h}})$$ (Notice how $$\color{blue} \text{width}$$ and $$\color{red} \text{length}$$ in the triangle formula become $$\color{red} \text{base}$$ and $$\color{blue} \text{height}$$. These words are used interchangeably.)

$${\text{A}}=\dfrac{1}{2}(5\times 7)$$

$${\text{A}}=\dfrac{1}{2}(35)$$

$${\text{A}}=17.5$$

So the area of the rectangle is $$17.5 \text{ in}^{2}$$. Remember to label the area with $$\text{in}^{2}$$ since we are measuring area in terms of inches.
)
3. A right triangle has perpendicular adjacent sides of lengths 21 cm and 25 cm. Use the formula for the area of a triangle to calculate the area of this triangle. Round to the nearest tenth. (
Solution
Solution:
$$262.5 \text{ cm}^{2}$$
)
4. The top of a slice of blueberry pie is in the shape of a triangle. The slice is 4 inches wide at the widest point and is 7 inches long. Use the formula for the area of a triangle to determine the surface area of the top of this slice of blueberry pie. (
Video Solution
Solution: $$14 \text{ in}^{2}$$
Details:

(Video Source | Transcript)
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5. A garden that is in the shape of a triangle has a width of 35 ft and a length of 55 ft. Use the formula for the area of a triangle to determine the area of this garden. Round to the nearest whole number. (
Solution
Solution: $$963 \text{ ft}^{2}$$
Details:
We are trying to find the area of a garden shaped like a triangle with a $$\color{blue} \text{width (or base) of 35 ft}$$ and a $$\color{red} \text{length (or height) of 55 ft}$$.

Remember, the area of a triangle is half the area of a rectangle with the same length and width.

When we find the area of a rectangle, we multiply the length times the width. To find the area of a triangle, we multiply the length times the width and divide it by two. We often refer to the '$$\color{blue} \text{width}$$' and ‘$$\color{red} \text{length}$$’ by the terms '$$\color{red} \text{base}$$’ and '$$\color{blue} \text{height}$$' when talking about triangles.

So, in this case, we would multiply 35 by 55, then divide it by 2.

$${\text{A}}=\dfrac{1}{2}(35\times55)$$

$${\text{A}}=\dfrac{1}{2}(1925)$$

$${\text{A}}=962.5$$

So the area of the garden is about $$963 \text{ ft}^{2}$$ when rounded to the nearest whole number. And remember, it is labeled $$\text{ft}^{2}$$ because we are measuring area in terms of square feet (ft).
)
6. A large triangular window has a base of 3 m and a height of 4 m. Use the formula for the area of a triangle to calculate the area of this window. (
Video Solution
Solution: $$6 \:{\text{m}}^{2}$$
Details:

(Video Source | Transcript)
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