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 form 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(b_{1} + b_{2})h A = ½(8.27 + 3.41) × 6.68 A ≈ 39 units^{2} |