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:

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:

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:

Therefore:

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