How to find the area of a trapezoid using the formula

Key takeaway: The trapezoid area formula is one of those geometry formulas that works best when you keep the labels straight. Once you know which sides are the bases and which measurement is the height, the calculation is simple.

The area of a trapezoid is given by

$A=\frac{a+b}{2}h$

where:

• $a$ = length of base 1
• $b$ = length of base 2
• $h$ = height

What the formula means

Add the two parallel sides first, divide by 2, then multiply by the height.

Why it works

The average of the two bases is

$\frac{a+b}{2}$

and the area is that average base length times the height.

Final form

$\boxed{A=\frac{a+b}{2}h}$

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Pitfalls the pros know 👇 A frequent mistake is using a slanted side as the height. The height must be the perpendicular distance between the two bases, not just any side length.

What if the problem changes? If you know the area and one base instead, you can rearrange the formula to solve for the missing value:

$h=\frac{2A}{a+b}$

or

$a=\frac{2A}{h}-b$

Tags: trapezoid area, base lengths, height of a trapezoid