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# Find the Height of a Triangle

## How to do it, given Area

Object of this page To practice applying the conventional area of a triangle formula to find the height, given the triangle's area and a base.
Example 1
In this triangle, the area is 17.7 square units, and its base is 4.

Let's find the height of this triangle, which is pictured below.
 The red measurements are the ones that are relevant to this problem. Remember that each triangle has 3 base/height pairs. So whenever you are talking about the height, we have to make sure we know which of the 3 'bases' (or sides) of the the triangle we are talking about. We can tell from the picture, that the height is perpendicular to the base whose measure is 4. That is why the side of length 4 is the base and the other sides do not affect this problem.
Steps to Find Area
 Step 1) Substitute known values into the area formula Area = $$\frac{1}{2} \cdot base \cdot height$$ 17.7 = ½(4)(h) Step 2) Find the height by solving for 'h' $$17.7 = 2h \\ h = \frac{17.7}{2} = 8.85$$

Practice Problems

Problem 1)
 If the area of the triangle on the left is 658.8square feet and its base is 24 inches, what is the height?

Problem 2)
 If the Area of the triangle on the left is 11.6 square units and its base is 4, what is its height?

Problem 3)
 If the Area of the triangle on the left is 17.7 square units and its base is 15, what is its height?

Problem 4)
 If the Area of the triangle on the left is 35.8. square units,find its height.