Area of a Right Triangle – Formulas and Examples

The area of a right triangle is the region covered by the 2D figure. Recall that a right triangle is a triangle that has a right angle, that is, a 90-degree angle. To calculate the area of these triangles, we can use the length of their base and the length of their height. Thus, we find the area by dividing the product of the height and the base by 2.

In this article, we will look at the formula for the area of a right triangle. In addition, we will use this formula to solve some problems.

GEOMETRY
formula for the area of a right triangle

Relevant for

Learning about the area of a right triangle with examples.

See examples

GEOMETRY
formula for the area of a right triangle

Relevant for

Learning about the area of a right triangle with examples.

See examples

Formula for the area of a right triangle

The area is a two-dimensional region and is measured in square units. The area can be defined as the amount of space taken up by the two-dimensional object.

The area of a right triangle can be calculated by using the following formula:

A= \frac{b \times h}{2}

where b is the length of the triangle’s base and h is the length of the height.

diagram of a right triangle

Derivation of the area formula

We are going to derive the area of a right triangle using the following diagram:

diagram of a right triangle and a rectangle

On the left side of the diagram, we have a right triangle. On the right side, we duplicate that triangle to form a rectangle. The height of the rectangle is equal to the height of the triangle and the base of the rectangle is also equal to the base of the triangle. Therefore, the area of the rectangle is:

 \text{Area}=\text{base}\times \text{height}

A=b\times h

Therefore, the area of a right triangle will be half the area of a rectangle:

A=\frac{b\times h}{2}


Area of a right triangle – Examples with answers

The following examples for right triangles are solved using the formula above. Each example has its respective solution, but it is recommended that you try to solve the exercises yourself before looking at the answer.

EXAMPLE 1

What is the area of a triangle that has a base of 8 m and a height of 10 m?

We have the following values:

  • Height, h=10
  • Base, b=8

Using these values in the formula, we have:

A= \frac{bh}{2}

A=\frac{(8)(10)}{2}

A=\frac{80}{2}

A=40

The area of the triangle is 40 m².

EXAMPLE 2

A triangle has a base of 16 m and a height of 10 m. What is its area?

We have the following information:

  • Height, h=10 m
  • Base, b=16 m

Substituting these values in the formula, we have:

A= \frac{bh}{2}

A=\frac{(16)(10)}{2}

A=\frac{160}{2}

A=80

The area of the triangle is 80 m².

EXAMPLE 3

The base of a right triangle is 15 m and its height is 11 m. What is its area?

We can identify the following information:

  • Height, h=11 m
  • Base, b=16 m

Using the area formula with these values, we have:

A= \frac{bh}{2}

A=\frac{(15)(11)}{2}

A=\frac{165}{2}

A=82.5

The area of the triangle is 82.5 m².

EXAMPLE 4

A right triangle has an area of 96 m² and a base of 8 m. What is its height?

In this case, we start with the area and we want to find the height. Therefore, we recognize the following values:

  • Area, A=96
  • Base, b=8 m

We use these values in the formula and solve for h:

A= \frac{bh}{2}

96=\frac{8h}{2}

192=8h

h=24

The height of the triangle is 24 m.

EXAMPLE 5

A triangle has an area of 120 m² and a height of 20 m. What is the length of its base?

Again, we start with the area, but now we want to find the base. Therefore, we use the following values:

  • Area, A=120
  • Base, b=20 m

We plug these values into the formula and solve for b:

A= \frac{bh}{2}

120=\frac{20b}{2}

240=20b

b=12

The base of the triangle is 12 m.


Area of a right triangle – Practice problems

Test your knowledge about the area of right triangles to solve the following problems. If you need help with this, you can look at the examples outlined above.

What is the area of a triangle that has a base of 6m and a height of 8m?

Choose an answer






What is the area of a triangle that has a base of 12m and a height of 14m?

Choose an answer






A triangle has an area of 100 {{m}^2} and a base of 20m. What is its height?

Choose an answer






What is the length of the base of a triangle that has an area of 84 {{m}^2} and a height of 21m?

Choose an answer







See also

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