The area of a trapezoid is found using the formula:
Area=(a+b)2×h\text{Area}=\frac{(a+b)}{2}\times hArea=2(a+b)×h
where aaa and bbb are the lengths of the two parallel sides (the bases), and hhh is the height (the perpendicular distance between these bases).
Explanation of the formula:
- The trapezoid is a quadrilateral with one pair of parallel sides, called bases.
- The height is the perpendicular distance connecting the two bases.
- The area formula calculates the average length of the two bases (a+b)2\frac{(a+b)}{2}2(a+b), then multiplies by the height hhh, essentially finding the area by treating the trapezoid as a rectangle with the average base length.
- This formula works regardless of whether the trapezoid is oriented normally or upside down.
Steps to find the area:
- Measure the two parallel sides: aaa and bbb.
- Measure the height hhh, which is the perpendicular distance between these bases.
- Substitute the values into the formula (a+b)2×h\frac{(a+b)}{2}\times h2(a+b)×h.
- Calculate to get the area in square units.
Example: If the bases are 7 cm and 13 cm, and the height is 5 cm, the area calculation is:
7+132×5=202×5=10×5=50 cm2\frac{7+13}{2}\times 5=\frac{20}{2}\times 5=10\times 5=50\text{ cm}^227+13×5=220×5=10×5=50 cm2
This formula can be applied similarly for any trapezoid.
This is the standard and most effective way to find the area of a trapezoid.
