Area of a Triangle Calculator

Published on: June 16, 2024
Final Answer: Free • Full Steps: Plus

This Area of a Triangle Calculator finds the space inside a triangle from its base and its perpendicular height, and shows the working line by line. Any triangle fills exactly half of the rectangle drawn on the same base and height, so the base is multiplied by the height and that product is then halved. The answer is written in square units. Following the same pattern every time is what makes the area of a triangle easy to picture, check, and work out on your own.

Triangle with base b and height h

In the diagram, the base is \(b\) and the height is \(h\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base and the height into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area.

Formula:

\(A = \tfrac{1}{2}bh\)
See Example 1 Hide Example 1

Problem

\(b = 8, h = 6\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base and the height into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the area of a triangle whose base is \(b = 8\) and whose height is \(h = 6\).

\(b = 8,\; h = 6\)

Step 2

Step 2 - Write the formula.

In this problem: A triangle fills exactly half of the rectangle drawn on the same base and height, so its area is half of the base multiplied by the height.

\(A = \tfrac{1}{2}bh\)

Step 3

Step 3 - Substitute the base and the height into the formula.

In this problem: Replacing \(b\) with \(8\) and \(h\) with \(6\) in \(A = \tfrac{1}{2}bh\) gives \(A = \tfrac{1}{2} \times 8 \times 6\).

\(A = \tfrac{1}{2} \times 8 \times 6\)

Step 4

Step 4 - Multiply the base by the height.

In this problem: Multiplying the base by the height gives \(8 \times 6 = 48\).

\(A = \tfrac{1}{2} \times 48\)

Step 5

Step 5 - Halve that product to get the area.

In this problem: Halving that product gives \(48 \div 2 = 24\).

\(A = \tfrac{1}{2} \times 48 = 24\)

Final Answer

\(A = 24\)
See Example 2 Hide Example 2

Problem

\(b = 2.5, h = 3\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the base and the height into the formula.
  4. Multiply the base by the height.
  5. Halve that product to get the area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the area of a triangle whose base is \(b = 2.5\) and whose height is \(h = 3\).

\(b = 2.5,\; h = 3\)

Step 2

Step 2 - Write the formula.

In this problem: A triangle fills exactly half of the rectangle drawn on the same base and height, so its area is half of the base multiplied by the height.

\(A = \tfrac{1}{2}bh\)

Step 3

Step 3 - Substitute the base and the height into the formula.

In this problem: Replacing \(b\) with \(2.5\) and \(h\) with \(3\) in \(A = \tfrac{1}{2}bh\) gives \(A = \tfrac{1}{2} \times 2.5 \times 3\).

\(A = \tfrac{1}{2} \times 2.5 \times 3\)

Step 4

Step 4 - Multiply the base by the height.

In this problem: Multiplying the base by the height gives \(2.5 \times 3 = 7.5\).

\(A = \tfrac{1}{2} \times 7.5\)

Step 5

Step 5 - Halve that product to get the area.

In this problem: Halving that product gives \(7.5 \div 2 = 3.75\).

\(A = \tfrac{1}{2} \times 7.5 = 3.75\)

Final Answer

\(A = 3.75\)

Example Problems

Click one to load it into the box and solve it.