Trapezoid Calculator

A trapezoid is defined by two parallel bases ($a$ and $b$) and two legs ($c$ and $d$). The area ($A$) is derived by multiplying the average of the two bases by the perpendicular height ($h$): $A = \frac{base_a + base_b}{2} \times height_h$. The perimeter ($P$) is simply the sum of all boundary sides: $P = base_a + base_b + leg_c + leg_d$. The median, representing the parallel segment halfway between the bases, equals the average of the two bases: $median = \frac{base_a + base_b}{2}$. Internal angles adhere to specific geometric rules, where adjacent angles between the parallel bases sum up to 180 degrees ($\pi$ radians).

Let us calculate the properties of a trapezoid with a bottom base ($base_a$) of 10 inches, a top base ($base_b$) of 6 inches, and a height ($height_h$) of 4 inches. First, find the area by averaging the bases: $(10 + 6) / 2 = 8$. Multiply this average by the height: $8 \times 4 = 32$ square inches. Next, find the median, which is also 8 inches. If the two legs are equal at 5 inches each, the perimeter is calculated by adding all sides together: $10 + 6 + 5 + 5 = 26$ inches. Our calculator automatically handles these formulas simultaneously for any given combination of known variables.

Always verify your units before inputting values; mixing inches and centimeters will corrupt your results. When dealing with right trapezoids, remember that one leg is perpendicular to both bases, meaning its length equals the height of the trapezoid. Double-check your angle inputs, as internal angles adjacent to the same leg must always supplement to 180 degrees.