How to Find the Area of a Square When Cut By a Diagonal Line

A square has four identical sides connected by four right, or 90-degree, angles. When a straight line diagonally crosses the square, one of the shapes the line creates from the square is a triangle. By employing the triangular area formula, where area = 1/2 * base measurement * height measurement, and the area of a square, where area = side length measurement ^2, you can find the two areas of the square separated by the diagonal line.

Things You'll Need

• Ruler
• Calculator

Instructions

Area Created by Diagonal

1. Measure the side lengths of the triangular shape created by the diagonal. For this example, the original square has a side length of 10. The diagonal creates a triangle with one side measuring 3 and the other measuring 6.

2. Multiply the two measured triangular sides together and then divide in half to calculate the area of the diagonally created triangle. For this example, multiplying 6 by 3 results in 18, and half of 18 is 9.

3. Calculate the area of the original square, and then subtract the triangular area from the square area to calculate the other area created by the diagonal line. In this example, the square's area is 10 multiplied by 10, which is 100. Subtracting 9 from 100 results in 91. The other area affected by the diagonal line is 91.

Tips & Warnings

• If the diagonal line is a proper square diagonal, meaning it traverses opposite corners, then just calculate half of the square's area since the line creates two identical triangles.

References

• Math Open Reference: Square
• Wolfram MathWorld: Square
• Math.com: Area Formulas