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

Video Source (05:49 mins) | Transcript

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

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.

Additional Resources

• Khan Academy: Area of a Triangle (5:29 mins | Transcript)

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

   x

   Solution:
   \(60 \text{ mm}^{2}\)
   )
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

   x

   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

   x

   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

   x

   Solution: \(14 \text{ in}^{2}\)
   Details:
   

   
   (Video Source | Transcript)
   )
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

   x

   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

   x

   Solution: \(6 \:{\text{m}}^{2}\)
   Details:
   

   
   (Video Source | Transcript)
   )

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