Where is the base of an isosceles trapezoid?

This isosceles trapezoid area calculator will help you deal with these very particular trapezoids. Recall that we say that a trapezoid is isosceles if its legs have the same length. You'll experience no trouble using Omni's isosceles trapezoid area calculator, but we know that life is hard and you sometimes have to calculate with pen and paper. Don't worry — we will teach you how to find the area of an isosceles trapezoid with the help of dedicated formulas.

What is the area of an isosceles trapezoid?

There are several dedicated isosceles trapezoid area formulas:

• bases a,b and height h given: A = (a + b) * h / 2

• bases a,b and leg c given: compute h via the Pythagorean Theorem (h is the square root of c² - (a-b)²/4) and A = (a + b) * h / 2

• bases a,b and angle h0 given: compute h as h2 and then A = (a + b) * h / 2

• base h4, leg c and angle h0 given: compute h as h8 and h9 as A = (a + b) * h / 20, then A = (a + b) * h / 2

Choose the isosceles trapezoid area formula that suits the data that is available (for notation, see the picture below). Or just use our isosceles trapezoid area calculator!

Useful trapezoid resources

Besides the isosceles trapezoid area calculator, Omni has a vast collection of trapezoid-related tools. Make sure to take a look at:

An isosceles trapezoid (called an isosceles trapezium by the British; Bronshtein and Semendyayev 1997, p. 174) is trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.

From the Pythagorean theorem,

(1)

so

(2)

(3)

An isosceles trapezoid has perimeter

(4)

and diagonal lengths

(5)

Longer Base

$$B$$

Shorter Base

$$b$$

Height

$$h$$

Oblique Side

$$S$$

Oblique side Projection

$$p_{1}$$

Diagonal

$$d$$

$$2p = B + b + 2S$$

Perimeter

$$A = \frac{\left(B + b \right) \times h}{2}$$

Area

$$B + b = \frac{2A}{h}$$

Sum of bases

$$h = \frac{2A}{B + b}$$

Height

$$B + b = 2p - 2S$$

Sum of bases

$$S = \frac{2p - B - b}{2}$$

Oblique Side

$$p_{1} = \frac{ B - b }{2}$$

Oblique side Projection

$$B - b = 2 \times p_{1}$$

Difference of bases

$$B = b + 2p_{1}$$

Longer Base

$$b = B - 2p_{1}$$

Shorter Base

Right Tr. delimited by height - oblique side

$$S = \sqrt{ {p_{1}}^2 + {h}^2 }$$

Side (Pythagoras' theorem)

$$h = \sqrt{ {S}^2 - {p_{1}}^2 }$$

Height

$$p_{1} = \sqrt{ {S}^2 - {h}^2 }$$

Oblique side Projection

Definition

An isosceles trapezoid is a trapezoid with oblique sides congruent.

Properties

1. The oblique sides are congruent
2. The angles adjacent to their respective bases are congruent
3. Diagonals are congruent
4. All the  Generic Trapezoid formulas are valid

Isosceles Trapezoid Formulas

What is the base angles of an isosceles trapezoid?

How do you find the legs of an isosceles trapezoid with bases?