Back
Area of a Triangle
> ... Math > Perimeter, Area, Volume > Area of a Triangle

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

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

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.
    This is a picture of a right triangle with a base that measures 5 in and a height that measures 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:
    This is a picture of a rectangle with a width of 5 inches and a length of 7 inches. There is a diagonal line from one corner to the opposite corner so that it is cut into two equivalent triangles.

    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 \(\color{red} \text{length (or height) of 55 ft}\).
    This is a picture of a right triangle with a width (or base) of 35 feet, and a length (or height) of 55 feet.

    Remember, the area of a triangle is half the area of a rectangle with the same length and width.
    This is a picture of a rectangle with a width of 35 feet and a length of 55 feet with a diagonal line from one corner to the opposite corner.

    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)
    )

Need More Help?


  1. Study other Math Lessons in the Resource Center.
  2. Visit the Online Tutoring Resources in the Resource Center.
  3. Contact your Instructor.
  4. If you still need help, Schedule a Tutor.