Question

how do the areas of triangle abc and def compare?
the area of (\triangle abc) is 1 square unit less than the area of (\triangle def).
the area of (\triangle abc) is equal to the area of (\triangle def).
the area of (\triangle abc) is 1 square unit greater than the area of (\triangle def).
the area of (\triangle abc) is 2 square units greater than the area of (\triangle def).

Explanation:

Step1: Calculate the area of \(\triangle ABC\)

Use the formula for the area of a triangle \(A=\frac{1}{2}\times base\times height\).
For \(\triangle ABC\), the base \(AB = 4\) (from \(x = 3\) to \(x = 7\)) and the height is \(4\) (from \(y = 2\) to \(y = 6\)).
\(A_{ABC}=\frac{1}{2}\times4\times4 = 8\)

Step2: Calculate the area of \(\triangle DEF\)

For \(\triangle DEF\), the base \(DF=6\) (from \(x=-2\) to \(x = 4\)) and the height is \(3\) (from \(y=-3\) to \(y = 0\)).
\(A_{DEF}=\frac{1}{2}\times6\times2= 6\)

Answer:

The area of \(\triangle ABC\) is \(1\) square unit greater than the area of \(\triangle DEF\).