Question

how does the area of triangle abc compare to the area of parallelogram ghijk?
the area of \\( \triangle abc \\) is 2 square units greater than the area of parallelogram ghijk
the area of \\( \triangle abc \\) is 1 square unit greater than the area of parallelogram ghijk
the area of \\( \triangle abc \\) is equal to the area of parallelogram ghijk
the area of \\( \triangle abc \\) is 1 square unit less than the area of parallelogram ghijk

Explanation:

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

Use the formula for the area of a triangle \(A=\frac{1}{2}\times base\times height\).
The base of \(\triangle ABC\) (from \(x = 1\) to \(x=- 3\)) \(b = 4\) units, and the height (from \(y = 1\) to \(y=-5\)) \(h = 6\) units.
\(A_{\triangle ABC}=\frac{1}{2}\times4\times6=12\) square units.

Step2: Calculate the area of parallelogram \(GHIJK\)

Use the formula for the area of a parallelogram \(A = base\times height\).
The base of parallelogram \(GHIJK\) (from \(x=-3\) to \(x = - 1\)) \(b = 2\) units, and the height (from \(y = 1\) to \(y = 4\)) \(h = 3\) units.
\(A_{GHIJK}=2\times6 = 12\) square units.

Answer:

The area of \(\triangle ABC\) is equal to the area of parallelogram \(GHIJK\).