How to Find the Area of a Square with a Given Diagonal

When used in reference to geometric shapes, a diagonal is a straight line going from one vertex to another inside the shape. A vertex is the point at which two sides meet. Since a square has four equal sides and each of the four interior angles equals 90 degrees, it does not matter which diagonal you are given because all are equal. If you are given the diagonal, you can find the length of the square's sides, and from that the area.

Things You'll Need

• Calculator

Instructions

1. Figure the square root of 2 on your calculator by entering 2 and then pushing the square root button to get about 1.4142. The square root of two is the ratio between the diagonal length and the side length.

2. Divide the length of the diagonal by 1.4142 to find the length of one side of the square. For example, if the diagonal measures 28 inches, you would divide 28 inches by 1.4142 to find the side length equals 19.799 inches.

3. Multiply the side length by itself to find the area of the square. In this example, you would multiply 19.799 inches by 19.799 inches to get 392 square inches as the area of the square.

References

• Analyze Math: Geometry Problems on Squares
• Cool Math: Properties of a Square