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Isosceles Trapezoid Area Calculator

An isosceles trapezoid has congruent non-parallel legs of equal length ($c = d$) and symmetric base angles.

Calculated Area
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Base a Base b Leg c Leg c h

Isosceles Trapezoid Geometry and Formulas

An isosceles trapezoid is axially symmetric. Its non-parallel legs are equal in length, and both angles adjacent to either base are equal.

1. Height via Half-Base Difference

Dropping two perpendiculars creates two congruent right triangles on either side. Each triangle has a horizontal base equal to x = |a - b| / 2.

x = |a - b| / 2
h = √(c² - x²) (Triangle condition: c > x)

2. Area Formula

Area = ½ × (a + b) × h

3. Congruent Diagonals Formula

Both diagonals of an isosceles trapezoid are equal in length:

Diagonal d = √(a × b + c²)
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Frequently Asked Questions

What is the formula for the area of an isosceles trapezoid?
The formula is A = ½(a + b)h, where a and b are the parallel bases and h is the perpendicular height. The formula is the same as for any trapezoid.
How do you find the height of an isosceles trapezoid?
If the two bases and the equal leg length are known, subtract the shorter base from the longer base and divide the difference by two. Use the Pythagorean theorem to calculate the height: h = √(c² − ((a − b)/2)²), where c is the equal leg length.
Can you calculate the area of an isosceles trapezoid using its side lengths?
Yes. If both parallel bases and the equal non-parallel side lengths are known, you can calculate the height using the Pythagorean theorem, provided the measurements form a valid isosceles trapezoid.
Are the diagonals of an isosceles trapezoid equal?
Yes. The diagonals of an isosceles trapezoid have equal lengths because of its symmetry.
How do you find the perimeter of an isosceles trapezoid?
Add the two parallel bases and twice the equal leg length. The formula is P = a + b + 2c.
Can an isosceles trapezoid have a shorter top base than its bottom base?
Yes. The two parallel bases can have different lengths. The equal non-parallel sides create the symmetry that defines an isosceles trapezoid.