Triangle area 30 m², base 12 m, find the height Step by Step

Step by step

The question

Question: find the height h of a triangle with area 30 m² and base 12 m.

1 Write the rule

A triangle is half of the box around it.

So its area is half of base times height: A = ½ × b × h.

Now put the numbers in: A = 30 and b = 12.

12 × 12 × h = 30

Careful!

Do not forget the half.

The triangle is only half of the box.

Careful: not h = 30 ÷ 12 ✗

2 Half of the base

Half of 12 is 6.

122 = 6

So 6 × h = 30.

6 × h = 30

3 Remove the × 6

We want h by itself.

The times 6 is in the way.

To remove times 6, we divide by 6.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

6 × h6 = 306

6 divided by 6 is 1.

So just h is left.

30 divided by 6 is 5 m.

So the height is 5 m.

h = 5 m

4 Check

Let's check: half of base times height.

12 × 12 × 5 = 6 × 5 = 30

We get 30, the area.

So the height is right!

Let's look back.

First: write the rule.

Then: half of the base.

Then: remove the × 6.

Last: check.

Answer