# How to Find the Area and Perimeter of a Triangle

## Area and Perimeter of a Triangle

The **area** of a triangle is found by taking half of the product of the base and the height. The base of the triangle can be any of the sides, but the height must be perpendicular to the base.

The **perimeter** of a triangle is found by adding all the sides together, so side 1 plus side 2, plus the base, since those are the 3 sides. One way to remember the formula for the area of a triangle is that a triangle is half of a parallelogram.

If you can imagine drawing the rest of the parallelogram out here, you can see this triangle is half of a parallelogram. The area of a parallelogram is base times height, so the area of half of a parallelogram or a triangle is half base times height.

Now for an example. Find the area and perimeter of the following triangle. First let’s find the area. We’re going to start by writing our formula for area of a triangle. The area of a triangle is half the product of the base and the height.

Now we need to substitute our base and height. Area is 1/2. Again, the base can be any of the sides, but the height must be perpendicular to it, so start with the perpendicular height, right here, the 6 inches. It’s perpendicular to this base, 13 inches.

Therefore, our base is 13 inches, and our height is 6 inches, so we substitute 13 inches for base times 6 inches for our height. Now, since all we’re doing is multiplying, we can multiply in any order. We can take half of 13 and multiply that times 6, or we can take half of 6 and multiply that times 13, or we can do 13 times 6, and then take half of that product.

It’s whatever is easiest, and (to me) I think taking half of 6 would be the easiest, so I’m going to start by taking half of 6 inches. Half of 6 inches is 3 inches, times 13 inches. 3 inches times 13 inches is 39 inches squared. Now, for perimeter. Again, we’re going to start with our formula.

The perimeter of a triangle is the sum of all the sides. So 10 inches plus 8 inches, plus our base, 13 inches. We can, again, add this in any order that we want, so maybe we start with 10 inches plus 13 inches, 23 inches plus 8 inches. 23 plus 7 would be 30, and 8 is 1 more than that, so the perimeter is 31 inches.