Question

1. find the area of the given triangle.

a. 12 m²
b. 12.5 m²
c. 15 m²
d. 24 m²

Explanation:

Step1: Determine the base and height

The base of the triangle is \(b = 6m\).
Using the Pythagorean theorem for one of the right - angled sub - triangles (side \(5m\), half of the base \(3m\)), we find the height \(h\).
Let the height be \(h\), then \(h=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4m\) (by \(a^{2}+b^{2}=c^{2}\), here \(c = 5\), \(a=3\), \(b = h\)).

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\).
Substitute \(b = 6m\) and \(h = 4m\) into the formula: \(A=\frac{1}{2}\times6\times4\).
\(A = 12m^{2}\)

Answer:

A. \(12m^{2}\)