Content

• To step
• Method 1 of 2: Determining the height when the area and base are known
• Method 2 of 2: Finding the height of an equilateral triangle

To calculate the area of ​​a triangle, you need its height. If this information is not provided, you can easily calculate it based on what you do know! This article will teach you two different ways to find the height of a triangle, depending on what information you got.

To step

Method 1 of 2: Determining the height when the area and base are known

1. The formula for the area of ​​a triangle. This is A = 1/2 bra.
   • a = Area of ​​the triangle
   • b = Length of the base of the triangle
   • h = Height of the base of the triangle
2. Look at the triangle and determine which variables are known. In this case you already know the area, so a is equal to that value. You should also know the value of one of the sides; give that value to "" b ". If you don't know both values ​​or one of them, you need a different method.
   • Any side of the triangle can be the base, regardless of how the triangle is drawn. To imagine this, rotate the triangle in your mind until the side that is too familiar has become the bottom.
   • For example, if you know that the area of ​​a triangle equals 20, and one of its sides is 4, then: A = 20 and b = 4.
3. Use your values ​​in the equation A = 1/2 bra and calculate. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value is the height of your triangle!
   • In the example: 20 = 1/2 (4) h
   • 20 = 2h
   • 10 = h

Method 2 of 2: Finding the height of an equilateral triangle

1. The properties of an equilateral triangle. An equilateral triangle has three equal sides and three equal angles of 60 degrees each. If you divide an equilateral triangle in half, you will end up with two congruent right triangles.
   • In this example, we'll use an equilateral triangle with sides that are 8 in length.
2. The Pythagorean theorem. The Pythagorean theorem states that for a right triangle with sides of length a and b , and a hypotenuse with length c : a + b = c. We can use this theorem to find the height of our equilateral triangle!
3. Divide the equilateral triangle in half and assign values ​​to the variables a, b and c. Side a is equal to half the length of a side, and side b is the height of the triangle we want to solve.
   • So in the example holds: c = 8 and a = 4.
4. Enter the values ​​in the Pythagorean theorem and solve for b. First calculate the square of c and a by multiplying it by itself. Then subtract a from c.
   • 4 + b = 8
   • 16 + b = 64
   • b = 48
5. Find the square root of b to find the height of the triangle! Use the square root function on your calculator to find Sqrt (. The answer is the height of your equilateral triangle!
   • b = Sqrt (48) = 6,93