Question

what is the area of \\( \triangle def? \\)
\\( \bigcirc 4.5 \\) square units
\\( \bigcirc 6.36 \\) square units
\\( \bigcirc 9 \\) square units
\\( \bigcirc 22.95 \\) square units

Explanation:

Step1: Identify the base and height

The base of \(\triangle DEF\) is \(6\) units (length of \(EF\)) and the height is \(1.5\) units (perpendicular distance from \(D\) to \(EF\) as \(DG\) is perpendicular to \(EF\) and \(DG = 1.5\)).

Step2: Use the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). Substitute \(base = 6\) and \(height=1.5\) into the formula: \(A=\frac{1}{2}\times6\times1.5\).

Step3: Calculate the area

First, \(6\times1.5 = 9\). Then \(\frac{1}{2}\times9=4.5\). So the area of \(\triangle DEF\) is \(4.5\) square units.

Answer:

4.5 square units