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To find the area of a triangle, you must first choose a side to be the base. (You can use
any of the three sides.) Once you have chosen your base, the height is the distance from
the base to the top of the triangle. The area of the triangle is then equal to ½ the length
of the base times the length of the height. This is said more simply as, "The area is
½ base times height." You write the formula like this.
As an example, consider this triangle with a base of 8 centimeters and a height of 5
centimeters. Using the formula, the area of the triangle is ½ times 8 centimeters times
5 centimeters. We simplify this by multiplying the numbers together, and then multiplying
the units together. First we multiply the numbers: ½ times 8 times 5 is 20. Next, we
multiply the units: centimeter times centimeter is equal to centimeters squared. You indicate
this with the squared exponent.
It's essential to note that the area only depends on the base and the height. The lengths
of the other two sides are unimportant. If we keep the base and height fixed, but move
the top vertex left and right, then the PERIMETER changes, but the AREA remains the same.