Trapezoid Area

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

A =

a =

b =

h =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

A trapezoid's area is the average of its two parallel sides multiplied by the perpendicular distance between them. The proof fits in one picture: take a second, identical trapezoid, flip it upside down, and snug it against the first — together they form a parallelogram with base (a + b) and height h, so one trapezoid is half of that. Area rules of exactly this kind appear in the Rhind papyrus, where Egyptian scribes around 1550 BC computed the areas of tapering fields along the Nile.

The formula still earns its keep in civil engineering: a drainage channel with a 3 m bottom, a 5 m top, and a 1.2 m depth has a cross-section of (3 + 5)/2 × 1.2 = 4.8 m², the number that sets how much water it can carry. As always, h must be measured perpendicular to the parallel sides — never along a slanted leg.

Trapezoid Area

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

Where

$A$ = Area
$a$ = Parallel side a
$b$ = Parallel side b
$h$ = Height

Missing one of these? Work it out first, then come back

Area — Area of a Circle, Area of a Triangle
Parallel side a — Law of Sines, Triangle Area (Two Sides and Included Angle)
Parallel side b — Law of Sines, Triangle Area (Two Sides and Included Angle)
Height — Area of a Triangle, Parallelogram Area