Question

how does the area of triangle abc compare to 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 2 square units greater than 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 $\triangle ABC$

For $\triangle ABC$, assume base $b = 4$ (horizontal distance from $A$ to the vertical - line through $C$) and height $h = 4$ (vertical distance from $B$ to the horizontal - line through $A$). Then $A_{ABC}=\frac{1}{2}\times4\times4 = 8$ square units.

Step3: Count base and height for parallelogram $GHJK$

For parallelogram $GHJK$, base $b = 4$ (horizontal distance between $G$ and $H$) and height $h = 2$ (vertical distance between the parallel - lines containing $GK$ and $HJ$). Then $A_{GHJK}=4\times2=8$ square units.

Answer:

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