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Trapezoid calculator

Three tabs for trapezoid, right trapezoid and isosceles trapezoid: bases, legs, height, midline, perimeter, area, base angles and diagonals

Formula

S=\frac{(a+b)h}{2},\quad c=\sqrt{p^2+h^2}

S = (a + b)h/2, midline m = (a + b)/2

Enter any known values among bases a, b, legs c, d and height h.

abhLeft leg c

Presets

Tap an edge, angle or region to see how it is computed

Bases

Legs and height

Base angles

Perimeter, area, diagonals

Relationh3

S=\frac{(a+b)h}{2}\Rightarrow h=\frac{2S}{a+b}

Area S18

Perimeter P20

Midline m6

Height h3

a8b4h3c5d3m6∠A36.87∠B90∠C90∠D143.13P20S18AC8.544BD5

Steps

8 / 8

1Given
$a=8,\ b=4,\ h=3,\ c=5$
Collect the given quantities first.
2Horizontal offset
$p=4,\quad q=a-b-p=8-4-4=0$
The offset is the projection of the leg onto the base.
3Find side
$c=\sqrt{p^2+h^2}=5,\quad d=\sqrt{q^2+h^2}=3$
Substitute the known values into the side relation.
4Perimeter
$P=a+b+c+d=8+4+5+3=20$
Add all sides to get the perimeter.
5Area
$S=\frac{(a+b)h}{2}=\frac{(8+4)\times3}{2}=18$
Apply the area formula; the unit is squared.
6Midline
$m=\frac{a+b}{2}=\frac{8+4}{2}=6$
The midline is half the sum of the bases.
7Angle sum
$\angle A=36.87^\circ,\ \angle B=90^\circ,\ \angle C=90^\circ,\ \angle D=143.13^\circ$
Triangle angles sum to 180 degrees; an n-gon sums to (n-2) x 180.
8Result
$P=20,\ S=18,\ m=6,\ AC=8.544,\ BD=5$
Collect all computed quantities.

Concept

A trapezoid has exactly one pair of parallel sides called the bases; the other two sides are the legs.

The midline is parallel to the bases and half their sum, so area = midline x height.

Going further

Symmetry of the isosceles trapezoid: It is symmetric about the line joining the midpoints of the bases, so angles on the same base and the diagonals are equal.
Why right trapezoids help: Cutting along the perpendicular leg splits it into a rectangle and a right triangle, the classic auxiliary construction.
Trapezoid and midline: With m = (a + b)/2, S = mh. When a = b the trapezoid becomes a parallelogram and the formula still holds.

Common mistakes

The bases are the parallel sides; position matters, not length.
In a right trapezoid the perpendicular leg is exactly the height.
An isosceles trapezoid has equal legs; unequal legs mean it is not isosceles.

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