When finding the height of a triangle, you must first of all know the formula for finding the area of a triangle.

** Formula for finding the area of a triangle:**

A = 1/2 b × h

A = area of a triangle

b = base of the triangle

h = height of the triangle

Now, you have known the formula for finding the area of a triangle, let’s find the height.

Height of a triangle is the area of the triangle divided by half of the base. With this, you will find it very easy to find the height of a triangle.

A = 1/2 b × h

h = A/ 1/2b (making the “h” the subject of the formula.

When calculating or finding the height of a triangle, you must have the area and the base, inorder to get the height.

**Example 1:**

Find the height of a triangle, whose base is 10 cm, and area 50 cm.

**Solution**

A = 1/2 b × h

h = A / 1/2b

h = 50 / 1/2(10)

Calculate the half of the base first, before dividing.

h = 50 / 5

h = 10 cm

**Example 2:**

Find the height of a triangle whose area is 64 cm, and given it’s base 16 cm.

**Solution**

A = 1/2 b × h

h = A / 1/2b

h = 64 / 1/2(16)

h = 64 / 8

h = 8 cm.

**Example 3:**

Triangle ABC and triangle XYZ are said to have the same height. (Prove if the above statement is true or false). Given that ∆ ABC has an area 120 cm and it’s base 4 cm, while ∆ XYZ has an area 360 cm and it’s base 12 cm.

**Solution**

For triangle ABC

A = 1/2 b × h

h = A / 1/2b

h = 120 / 1/2(4)

h = 120 / 2

h = 60 cm

For triangle XYZ

A = 1/2 b × h

h = A / 1/2b

h = 360 / 1/2(12)

h = 360 / 6

h = 60 cm.

Therefore, the above statement which states that ∆ ABC and ∆ XYZ has the same height is true.

**Example 4:**

The area of triangle MNO is 49 cm and it’s base is 14 cm. Find it’s height.

** Solution**

A = 1/2 b × h

h = A / 1/2b

h = 49 / 1/2(14)

h = 49 / 7

h = 7 cm

**Example 5:**

Find the heights of these two triangles, ∆ PQR and ∆ EFG, having the same base(6 cm) but different areas.

Given: the area of ∆ PQR is 300cm, while the area of ∆ EFG is 96 cm.

**Solution**

For triangle PQR

A = 1/2 b × h

h = A / 1/2b

h = 300 / 1/2(6)

h = 300 / 3

h = 100 cm

For triangle EFG

A = 1/2 b × h

h = A / 1/2b

h = 96 / 1/2(6)

h = 96 / 3

h = 32 cm.

So you see, finding the height of a triangle is not a big deal, as long as you know the formula, you know the solution.