How To Find The Area Of A Rectangle Using The Diagonal 8 Steps

You’ll be able to see the 2 triangles that make up the rectangle now.

If you were working with a square, you could assign both sides of the triangle as a{\displaystyle a} since they are both the same. You can use the Pythagorean Theorem because you’re working with a right angle triangle.

Let’s say the diagonal is 10 inches and the length is 8 inches. The equation would look like this: a2+82=102{\displaystyle a^{2}+8^{2}=10^{2}}.

For example: a2+82=102{\displaystyle a^{2}+8^{2}=10^{2}}. a2+64=100{\displaystyle a^{2}+64=100}. a2=100−64{\displaystyle a^{2}=100-64}. a2=36{\displaystyle a^{2}=36}. a2=36{\displaystyle {\sqrt {a^{2}}}={\sqrt {36}}}. a=6{\displaystyle a=6}.

For example: A=8×6{\displaystyle A=8\times 6}. A=48 in2{\displaystyle A=48\ in^{2}}. Area is always in units squared.

It’s not mandatory to draw your triangle, but it can help you, especially if you’re just starting out.

For example, if the length is 8 inches and the diagonal is 10 inches, the formula would be A=8×102−82{\displaystyle A=8\times {\sqrt {10^{2}-8^{2}}}}.

A=8×102−82{\displaystyle A=8\times {\sqrt {10^{2}-8^{2}}}}. A=8×36{\displaystyle A=8\times {\sqrt {36}}}. A=8×6{\displaystyle A=8\times 6}. A=48{\displaystyle A=48}.