Triangle Area Calculation: Using 1/3 Ratio and 6-Unit Height

Question

Since the side BC is $\frac{1}{3}$ side AE.

Calculate the area of the triangle:

00:00 Calculate the triangle's area

00:05 BC equals one-third of AE according to the given data

00:10 Substitute in AE's value to determine BC

00:18 Apply the formula for calculating the area of a triangle

00:21 (base(BC) x height(AE)) divided by 2

00:27 Substitute in the relevant values and calculate to determine the area X

00:31 Reduce the 2

00:35 This is the solution

Let's calculate the area of triangle ABC by following these steps:

Step 1: Calculate AE using the ratio. Given that side BC is $\frac{1}{3}$ of AE, if we call AE = 6 (as shown or suggested by the illustration, considering AE is the vertical height), then $BC = \frac{1}{3} \times 6 = 2$ .
Step 2: The height of triangle ABC is given by the length AE, which is 6.
Step 3: Calculate the area using the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times BC \times AE = \frac{1}{2} \times 2 \times 6 = 6$ .

Therefore, the area of triangle ABC is $\text{6}$ .