How to Calculate the Area of a Triangle Part 2

By | November 2, 2014

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?

area of a 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?

area of a shaded part

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.

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