how do the areas of triangle abc and def compare? the area of △abc is 1 square unit less than the area of…

Answer:

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

Explanation:

Step1: Recall area formula

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

Step2: Find base and height of $\triangle ABC$

For $\triangle ABC$, assume the base $AB$ lies on the horizontal - grid. If we count the grid - squares, $AB = 4$ units and the height (vertical distance from $C$ to $AB$) is $4$ units. Then $A_{ABC}=\frac{1}{2}\times4\times4 = 8$ square units.

Step3: Find base and height of $\triangle DEF$

For $\triangle DEF$, assume the base $DF$ lies on the horizontal - grid. By counting the grid - squares, $DF = 4$ units and the height (vertical distance from $E$ to $DF$) is $4$ units. Then $A_{DEF}=\frac{1}{2}\times4\times4=8$ square units.

Step4: Compare the areas

Since $A_{ABC}=8$ square units and $A_{DEF}=8$ square units, the area of $\triangle ABC$ is equal to the area of $\triangle DEF$.