Question

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

Explanation:

Step1: Recall area formula for triangle

$A=\frac{1}{2}bh$, where $b$ is base and $h$ is height.

Step2: Calculate area of $\triangle LMN$

Count grid - squares. Base $b = 4$ units, height $h = 3$ units. $A_{LMN}=\frac{1}{2}\times4\times3 = 6$ square units.

Step3: Calculate area of $\triangle RST$

Base $b = 4$ units, height $h = 4$ units. $A_{RST}=\frac{1}{2}\times4\times4=8$ square units.

Step4: Compare areas

$A_{RST}-A_{LMN}=8 - 6=2$ square units. So the area of $\triangle RST$ is 2 square units greater than the area of $\triangle LMN$.

Answer:

The area of $\triangle RST$ is 2 square units greater than the area of $\triangle LMN$.