 When we're looking to find the area of a trapezoid, first remember that a trapezoid has only one pair of Parallel sides, and so we call those the two bases. Maybe I'll call this base 1, and I'll call this base 2, and the height of a trapezoid is always perpendicular to the two bases, so the distance between the two bases and perpendicular to both bases. So that would be the height, and the area of a trapezoid is one-half times the quantity B1 plus B2, in other words, the sum of the bases times the height. So once again, we've got area is the sum of the bases times height times one-half. So let's apply that to an example problem. Here we have a trapezoid, and we have the two bases. We have a base of 40 meters, and we have a base of 18, and the height, we see the height is 15. And so the area, first remember the area formula, and so we have to substituting the values. So area is one-half, and now it doesn't matter the order that you set B1 and B2. Just remember that you're adding the two bases, 40 plus 18 times the height, which was 15. 40 plus 18 is 58, and one-half of 58 is 29, and so we have a final area of 435 square meters. Let's try another quick example. In this case, we still have a trapezoid, although it's sort of lying on its side. Remember the bases are the two parallel sides. So my two bases are 12 and 24, and the height, even though the height is sort of denoted outside of the trapezoid, the height is the distance that's perpendicular to the two bases, and so that would be 28. And so our area is one-half times 24 plus 12, the two bases, times the height, which is 28, times 36, times 28, which, if you grab a calculator, that sets up as 504 square units. And let's just try one more example with trapezoids. So in this trapezoid, the problem is we don't know the height. We know this length 5, but 5 isn't the height because it's not it's not perpendicular to the two bases. Please note, because we have an isosceles trapezoid, this length is also 5. So in order to find the height, in other words, in order to find those dashed lines, first recognize that this length, this seven units, well, that seven units is the same as this seven units. And so the leftover pieces, in order to make a full 13, this length must be 3, and this length must be 3, right, because the entire length was 13. So this whole length is 13. We removed 7 from the middle, and 13 minus 7 is 6, and so we have 6 split into two equal parts. And now, if we consider, let's say we just look at this triangle, which refers to this triangle, we have 5, 3, and then the unknown height. Using the Pythagorean theorem, we can find the length of that height. 3 squared plus h squared is equal to 5 squared. Solving that for h gives you a height of 4 units. So our height here is 4. And so now we can find, we can just substitute in values to the area formula. So we know that the area is 1 half times the two bases, the longer one was 13, the shorter one up top was 7, times the height, which we found to be 4. And if you plug that in your calculator, you get that the area is 40 square units. All thanks to Pythagoras. Thank you Pythagorean theorem.