Question

how does the area of triangle rst compare to the area of triangle lmn? the area of △rst is 2 square units less than the area of △lmn. the area of △rst is equal to the area of △lmn. the area of △rst is 2 square units greater than the area of △lmn. the area of △rst is 4 square units greater than the area of △lmn.

Explanation:

Step1: Recall area formula for triangle

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Find area of $\triangle{RST}$

For $\triangle{RST}$, assume base along $x -$ axis. Base $b = 4$ (from $x = 1$ to $x = 5$) and height $h= 2$ (from $y = 1$ to $y = 3$). So $A_{RST}=\frac{1}{2}\times4\times2=4$ square units.

Step3: Find area of $\triangle{LMN}$

For $\triangle{LMN}$, assume base along $x -$ axis. Base $b = 4$ (from $x=- 3$ to $x = 1$) and height $h = 2$ (from $y=-2$ to $y = 0$). So $A_{LMN}=\frac{1}{2}\times4\times2 = 4$ square units.

Answer:

The area of $\triangle{RST}$ is equal to the area of $\triangle{LMN}$.