AREA OF A TRAPEZOID

A trapezoid looks like this:

A trapezoid has two parallel sides. In this case they are labeled B1 and B2. The other two sides are labeled C and D. How can we calculate its area? Well we know how to calculate the area of a rectangle and the area of a triangle. Can we turn the trapezoid into rectangles and triangles and add their areas?

We can break the trapezoid into three pieces. They will look like this:

So now, instead of a trapezoid, we have a rectangle R, and two triangles T1 and T2. The area of the trapezoid is equal to the sum of the areas of R, T1 and T2. We can see that side B1 of the trapezoid has been broken into 3 parts, x, B2 and y. So we know B1 = x + y + B2.

Remember when we calculated the area of a triangle we first made the triangle into a rectangle that had 2 times the area of
the triangle.

We can do the same thing here. So now, our trapezoid will look like this:

We now have 3 rectangles, R1 with area Ax, R with area AB2 and R2 with area Ay. The area of the trapezoid is less than this because we turned the triangles into rectangles but we will divide that back out in a minute. Lets move these rectangles around to make things easier to see:

Now we have two rectangles. The one on the left has area A(x+y) and we need half of that (the area of triangles T1 and T2) so we can

write What does this mean? . All that's left to do is simplify the formula using the fact that
B1 = x + y +B2 or (using a little algebra) x + y = B 1- B2. So here are a few steps in algebra to get to the final formula:

step 1 step 2 step 3 Are the steps confusing?

When all the details are figured out, we get the formula: so in our original trapezoid if B1 = 14 centimeters and B2 = 10

centimeters and A = 8 centimeters, what is the area of the trapezoid? Wizard please:

Here's a calculator to help you:

To practice calculating the area of a trapeziod go to this website. Here is another good practice website.

Would you like to check your understanding of polygons? Try this