How to Get the Perimeter of a Triangle if the Area Is Given

Area, Base and Height

• 1

  Write out the formula. Area = 1/2(base)(height), or A = 1/2bh.

• 2

  Rewrite the formula on the next line, this time filling in the information you have: the area, and either the base or the height of the triangle. So, if the area is 30 and the base is 12, you'll write: 30 = 1/2(12)h.

• 3

  Work the algebra problem to solve for the missing variable. In the example above, your third line should read 30 = 6h, because you multiplied 1/2 by 12. Your fourth line should read 5=h, because you divided 30 by 6. Five is the height.

Pythagorean Theorem

• 4

  Write the Pythagorean Theorem: A squared + b squared = c squared.

• 5

  Fill in the formula with the information you have, rewriting it on the next line. The hypotenuse, or the longest side, is also the side opposite the right angle and is always represented by "c." In the example above, you would write 5 squared + 12 squared = c squared.

• 6

  Work the problem, solving for c. The third line, using the example, would read 25 + 144 = c squared, because you squared both 5 and 12. The fourth line should read 169 = c squared, after adding 25 and 144. The fifth line should read 13 = c, since you took the square root of 169.

Adding the Sides

• 7

  Write the formula for finding the perimeter of a triangle, p = a+b+c.

• 8

  Plug in the appropriate numbers on the next line. Using the example, you'd write p = 5+12+13.

• 9

  Solve for p. Using the example, your third line should read p = 30, since you added 5, 12 and 13. The perimeter is 30.