# How to Calculate the Diameter of a Rectangle ••• kkant1937/iStock/GettyImages

A rectangle is any flat shape with four straight sides and four 90 degree angles, or right angles. Each side of a rectangle joins with two right angles. The diameter of a rectangle is the length of a diagonal, or either of two long lines that join opposite corners. A diagonal divides a rectangle into two identical right angle triangles. In mathematics, the diagonal of a right angle triangle is called the hypotenuse. Use the Pythagorean theorem:

H^2 = A^2 + B^2

to determine the length of the diagonal and thus calculate the diameter of a rectangle.

Examine the T-square and make sure the two pieces meet at a 90 degree angle.

Draw any rectangle that fills about half a sheet of paper. Use the T-square as a guide to make all four angles right angles. Ensure that the opposite sides of your rectangle are parallel and of equal length.

Draw a diagonal between two opposite corners using the T-square.

Measure the length of each side to highest precision using the T-square, and write the values near the respective sides. Label the sides: mark any side "A," label the adjacent side (opposite the hypotenuse) "B," and make the hypotenuse "H."

Calculate the triangle's hypotenuse (diagonal) length using the equation:

H = \sqrt{A^2 + B^2}

derived from the Pythagorean theorem, to calculate the hypotenuse of the triangle. Square the values of A and B, then add the squares together. Calculate the value of H by using a calculator to find the square root of the resulting sum. The value of H, the length of the diagonal, is also the diameter of the rectangle formed by the two triangles.

Measure the length of the hypotenuse with the T-square and compare the measurement with the calculated value.

## Example Calculation

Example calculation: if A = 5.5 inches and B = 7.7 inches, then:

\begin{aligned} H^2 &= 5.5^2+ 7.7^2 \\ &= 30.25 + 59.29 \\ &= 89.54 \end{aligned}

Therefore:

\begin{aligned} H &= \sqrt{89.54} \\ &= 9.46 \text{ inches} \end{aligned}

Any difference between the lengths you obtain by measuring and those you calculate will reflect the precision of your drawing and measuring.

#### Things You'll Need

• Pencil
• Paper
• T-square or try square
• Calculator

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