Trapezoid calculator
This calculator finds the unknown element of a trapezoid given any three known values. The calculator can find long and short base, side, diagonal, height, median, area perimeter and interior angle. The calculator gives you a step-by-step solution on how to find the missing value.
Tutorial
What is a trapezoid?
The trapezoid is any quadrilateral with one pair of parallel sides. The special, and most important cases are the: right trapezoid (have two right angles), and the isosceles trapezoid (have two equal legs).
Trapezoid attributes
Most important formulas?
The calculator uses the following formulas to find the missing elements of a trapezoid.
1. Area
A = (a+b)h/2
2. Diagonal
d2 = h2 + y2
d2 = a2 + c2 - 2ac cos(α)
3. Leg
c2 = h2 + x2
4. Median
m = (a + b)/2
5. Median
α + β = 1800
6. Altitude
h = c·sin(α)
Learn how to prove the area trapezoid formula in 30 seconds.
Solved examples
Example 1:
Find the area of a trapezoid if the legs are a=10cm and b=6cm and the height is h=5cm.
A = (a+b)h/2
A = (10+6)·5/2
A = 16·5/2
A = 80/2
A = 40
Example 2:
Find the leg of a trapezoid if a=15cm, b=9cm and h=4cm.
Step 1: Find [MxM]:
x = (a-b)/2
x = (15-9)/2
x = 6/2
x = 3
Step 2: Find altitude h:
h2 = x2 + h2
h2 = 32 + 42
h2 = 9 + 16
h2 = 25
h = 5