Hi, I'm Rebecca Pierce for About.com, and today we're going to be finding the perimeter and surface area of a trapezoid.

Add All Side Lengths for the Perimeter

So here we have a trapezoid. A trapezoid is a four-sided shape. A and b are parallel and c and d are slanted. The perimeter of a trapezoid is simply the lengths of the sides of the trapezoid added together. So the length of a plus the length of b plus the length of c plus the length of d. So for our example, let's say that A is equal to four, and that C and D are both equal to three, and that B is equal to six. That gives that the perimeter is equal to four plus three plus three plus six, which is equal to sixteen.

The Formula for Surface Area of a Trapezoid is A=1/2(a+b)h

So now we're going to look at the origin of this formula. And to do this we're going to divide the trapezoid into three shapes that we already know how to deal with. So the area of the rectangle is a x h, where h is the height of your trapezoid. The two triangles we have are both right triangles, and they're both equal to each other. Thus, we can use the formula for the area of a right triangle, which is 1/2 x (b-a)/2 x h. So that means that our total area is equal to a x h, the area of the rectangle + (b-a)/2 x h, which is the area of the two triangles. And if you combine this for your grand total, you get 1/2(a+b)h, which is the formula we had at the beginning for the surface area of a trapezoid.

So now that we've gone through how to get the formula for a surface area, let's look at an example. And let's say that we have a is equal to four, both c and d are equal to three and b is equal to six and that the height, which is h, is equal to four. Plugging those numbers in to the surface area formula, we get: 1/2 x (4+3) x (4), which is equal to 1/2 x (7) x (4), which is equal to 14.

Thank you for watching, and for more info visit About.com.

Add All Side Lengths for the Perimeter

So here we have a trapezoid. A trapezoid is a four-sided shape. A and b are parallel and c and d are slanted. The perimeter of a trapezoid is simply the lengths of the sides of the trapezoid added together. So the length of a plus the length of b plus the length of c plus the length of d. So for our example, let's say that A is equal to four, and that C and D are both equal to three, and that B is equal to six. That gives that the perimeter is equal to four plus three plus three plus six, which is equal to sixteen.

The Formula for Surface Area of a Trapezoid is A=1/2(a+b)h

So now we're going to look at the origin of this formula. And to do this we're going to divide the trapezoid into three shapes that we already know how to deal with. So the area of the rectangle is a x h, where h is the height of your trapezoid. The two triangles we have are both right triangles, and they're both equal to each other. Thus, we can use the formula for the area of a right triangle, which is 1/2 x (b-a)/2 x h. So that means that our total area is equal to a x h, the area of the rectangle + (b-a)/2 x h, which is the area of the two triangles. And if you combine this for your grand total, you get 1/2(a+b)h, which is the formula we had at the beginning for the surface area of a trapezoid.

So now that we've gone through how to get the formula for a surface area, let's look at an example. And let's say that we have a is equal to four, both c and d are equal to three and b is equal to six and that the height, which is h, is equal to four. Plugging those numbers in to the surface area formula, we get: 1/2 x (4+3) x (4), which is equal to 1/2 x (7) x (4), which is equal to 14.

Thank you for watching, and for more info visit About.com.

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