Area of Trapezoids Examples

What is the area of this trapezoid?

We know the two bases are 7 cm and 10 cm long, and the height is 5 cm long. All we need to do is plug these bad boys into the formula.

A = ½(b₁ + b₂)h
A = ½(7 + 10) × 5
A = 42.5 cm²

A trapezoid's area is 144 mm² and its height is 8 mm. If one of its bases is five times the length of the other, what are the lengths of the bases?

We can use the area formula and solve for the two bases. But one equation and two unknowns? What will we ever do?

Well, we can relate the two bases to each other. If we let b₁ = x, we know that b₂ = 5x because it's five times as long as the other. If we plug in all these values and solve for x, we should be good to go.

A = ½(b₁ + b₂)h
144 = ½(x + 5x) × 8
144 = 4(x + 5x)
6x = 36
x = 6

Since we know that b₁ = x, we can say that b₁ = 6 mm and b₂ = 5x = 30 mm.

What is the area of this isosceles trapezoid?

We know the two bases of this isosceles trapezoid, but not its height. If you think that 70° angle has something to do with finding it, you're probably right.

If we draw the height, we can see that it will make a right triangle. Knowing the base of the triangle will allow us to use the tangent of that 70° angle to find the height. Luckily, an isosceles trapezoid means the sides of the bottom base that stick out past the top base are identical.

The base of our right triangle is (8.27 – 3.41) ÷ 2 = 2.43. If we dig back and remember that tangent means opposite over adjacent, we can set up this equation and solve it using our lovely calculators.

2.43 × tan(70°) = h
h ≈ 6.68 units

Now that we have the height and both bases, we can find the area using our trusty formula.

A = ½(b₁ + b₂)h
A = ½(8.27 + 3.41) × 6.68
A ≈ 39 units²