Question

Perimeter of \(\Delta ABC\) is 32 m. If AB = BC and altitude BD measures 8 m, find area of triangle ABC.

Hint:

For isosceles triangles, use symmetry to simplify calculations and find the area easily with base and height.

Answer 1

Step 1: Understanding the question.
We are given the perimeter of \(\Delta ABC\), the sides AB = BC, and the altitude BD = 8 m. We are asked to find the area of the triangle.
Step 2: Formula for the area of a triangle.
The area of a triangle is given by the formula:
\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \] Here, the base is AB (or BC), and the height is BD. Using the given perimeter, we can find the base and calculate the area.
Step 3: Conclusion.
The area of the triangle is \(\boxed{128 \, \text{m}^2}\).