how does the area of triangle rst compare to the area of triangle lmn? the area of △rst is 2 square units…

Answer:

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

Explanation:

Step1: Recall area formula

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

Step2: Find base and height of $\triangle{RST}$

Counting grid - squares, for $\triangle{RST}$, base $b_{1}=4$ (from $x = 1$ to $x = 5$) and height $h_{1}=3$ (from $y = 1$ to $y = 4$). Then $A_{1}=\frac{1}{2}\times4\times3 = 6$ square units.

Step3: Find base and height of $\triangle{LMN}$

For $\triangle{LMN}$, base $b_{2}=4$ (from $x=-3$ to $x = 1$) and height $h_{2}=3$ (from $y=-1$ to $y = 2$). Then $A_{2}=\frac{1}{2}\times4\times3=6$ square units.

Step4: Compare areas

Since $A_{1}=6$ and $A_{2}=6$, the area of $\triangle{RST}$ is equal to the area of $\triangle{LMN}$.