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In this lesson, we will learn about the area of a triangle.

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First, let's consider this parallelogram with the base B and the height H.

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Now, in the previous lesson, we learned that the area of a parallelogram, A = BH.

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Observe that, if we cut this parallelogram by half, and remove this portion, we now have a triangle with the base B and height H.

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Since the area of this triangle, is half of the area of a parallelogram, the formula for the area of this triangle, A = 1/2BH.

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Note that, it is very important to include the unit. Since this is the formula for area, its unit will be in the form of square unit.

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We will see more explanations on this, in the upcoming example.

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Now, let's see some examples on using this formula.

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Find the area of this triangle when its base is 5cm, and its height is 4cm.

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First, we start with the formula for the area of a triangle, A = 1/2BH.

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Since the base is given as 5cm, we can substitute B with 5.

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Similarly, since the height is given as 4cm, we can substitute H with 4.

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Next, we can simplify by multiplying 5, with 4. This gives 20.

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Note that, one half bracket 20, can be rewritten as, 1 bracket over 2.

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Let's continue. 1 multiply 20, gives back 20.

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20 divides by 2, gives 10.

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Note that, this number has no meaning unless we include the unit for it.

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Since the units are given in centimeter, the unit for the area will be in square centimeter.

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Hence, the area of this triangle is 10 square centimeter.

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Next example, given that the area of this triangle is 24 square feet, and its base is 6ft. Find its height.

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Again, we start with the formula for the area of a triangle, A = 1/2BH.

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Now, since the area, and the base are given, we can find the height by solving this equation for h. Here’s how.

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It is easier to work with this equation if we rewrite this term, one half BH as, 1 BH over 3. 1BH is the same as BH.

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Next, note that we can remove this fraction, by multiplying both sides of the equation with 2.

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By doing so, we have, 2A = BH.

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Next, since the area is given as 24, we can substitute 'A' with 24.

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2 multiply by 24, gives 48.

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Similarly, since the base is given as 6 feet, we can substitute B with 6.

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Now we have, 6h equals to 48.

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Let's rewrite this equation so that it will look neater.

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To find h, we need to remove 6. We can do so by dividing both sides of the equation with 6.

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By doing so, we have, H equals to 48 over 6.

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48 divides by 6, gives 8.

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Now, this number is meaningless unless we include the unit for it.

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Since the base is in feet, the height of the triangle will be in feet.

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Therefore, the height of this triangle is 8ft.

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That is all for this lesson. Try out the practice question to further your understanding.