## How to Calculate the Area of a Triangle Part 2

We continue our discussion on how to find the area of a triangle. In the previous post, we have learned where the formula for the area of a triangle came from. We have studied that a triangle with area $A$, base $b$ and height $h$ is $A = \displaystyle \frac{bh}{2}$

We continue our discussion with the third example in this series.

Example 3

What is the base of a height 7 and area 8.75 square centimeters?

Solution $A = \displaystyle \frac{bh}{2}$ $8.75 = \displaystyle \frac{b(7)}{2}$

Multiplying both sides by 2, we have $17.5 = 7b$.

Dividing both sides by 7 gives us $b = 2.5$.

Therefore, the height of the triangle is 2.5 cm.

Example 4

Two triangles are formed by drawing a diagonal from the opposite corners of a square. If the side length of the square is 8.4 cm, what is the area of each triangle? Solution 1

The area of a triangle is half the area of the square, so we can just find the area of a square and divide it by 2. If we let $A_1$ be the area of the square with side $s$, then $A_1 = s^2 = (8.4)^2 = 70.56$.

Now, since the area of the triangle is half the square, we divide 70.56 by 2 which is equal to 35.28.

So the area of the triangle is 35.28 square units.

Solution 2

The base and the height of the triangle are equal. So, $A = \displaystyle \frac{bh}{2}$ $A = \displaystyle \frac{(8.4)(8.4)}{2}$ $A = \displaystyle \frac{70.56}{2}$ $A = 35.28$.

So the area of the triangle is 35.28 square units.

Example 5

What is the area of the shaded part in the figure below if the side of the square is 8 cm? Solution

The area of the shaded part is half the area of the square. Since the area of the square is 8(8) = 64 square centimeters, the area of the shaded part is equal to 32 square units.

Can you find other solutions?

In the next post, we are going to have a quiz on what we have learned so far.