Question

how does the area of triangle abc compare to the area of parallelogram ghjk? the area of △abc is 2 square units greater than the area of parallelogram ghjk the area of △abc is 1 square unit greater than the area of parallelogram ghjk the area of △abc is equal to the area of parallelogram ghjk the area of △abc is 1 square unit less than the area of parallelogram ghjk

Explanation:

Step1: Recall area formulas

Area of a triangle $A_{triangle}=\frac{1}{2}bh$, area of a parallelogram $A_{parallelogram}=bh$.

Step2: Count base and height for $\triangle ABC$

Counting grid - squares, for $\triangle ABC$, base $b = 4$ (from $x = 2$ to $x=- 2$) and height $h = 6$ (from $y = 0$ to $y=-6$). Then $A_{ABC}=\frac{1}{2}\times4\times6 = 12$ square - units.

Step3: Count base and height for parallelogram $GHJK$

For parallelogram $GHJK$, base $b = 4$ (from $x=-2$ to $x = 2$) and height $h = 3$ (from $y = 1$ to $y = 4$). Then $A_{GHJK}=4\times3=12$ square - units.

Answer:

The area of $\triangle ABC$ is equal to the area of parallelogram $GHJK$