Question

how do the areas of triangle abc and def compare? the area of △abc is 1 square unit less than the area of △def. the area of △abc is equal to the area of △def. the area of △abc is 1 square unit greater than the area of △def. the area of △abc is 2 square units greater than the area of △def.

Explanation:

Step1: Find base and height of △ABC

From the graph, for △ABC, base \(AB = 4 - 3=1\) unit and height \(h_{ABC}=6 - 2 = 4\) units.

Step2: Calculate area of △ABC

Using the triangle - area formula \(A=\frac{1}{2}\times base\times height\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\) square units.

Step3: Find base and height of △DEF

For △DEF, base \(DF=4-(-2)=6\) units and height \(h_{DEF}= - 1-(-3)=2\) units.

Step4: Calculate area of △DEF

Using the triangle - area formula \(A=\frac{1}{2}\times base\times height\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) square units.

Step5: Compare the areas

\(A_{DEF}-A_{ABC}=6 - 2=4\) (This is wrong above, let's correct it).
For △ABC: base \(AB = 4 - 3 = 1\), height \(h = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1 - (-3)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2 = 6\) (Wrong, recalculate).
For △ABC: base \(AB = 4 - 3=1\), height \(h = 6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: \(A_{ABC}=\frac{1}{2}\times(4 - 3)\times(6 - 2)=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC: base \(AB = 4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h = 0 - (- 2)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF: base \(DF=4 - (-2)=6\), height \(h = 0-(-2)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h = 0-(-2)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 3 - 3=0\) (wrong), base \(AB=4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC:
Base \(AB = 4 - 3=1\), height \(h = 6 - 2=4\). Using the area formula \(A=\frac{1}{2}\times base\times height\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\). Using the area formula \(A=\frac{1}{2}\times base\times height\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC:
Base \(AB = 4 - 3 = 1\), height \(h=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF:
Base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2 = 6\) (wrong).
For △ABC:
Base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC:
Base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC:
Base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2 = 6\) (wrong).
For △ABC:

Answer:

Step1: Find base and height of △ABC

From the graph, for △ABC, base \(AB = 4 - 3=1\) unit and height \(h_{ABC}=6 - 2 = 4\) units.

Step2: Calculate area of △ABC

Using the triangle - area formula \(A=\frac{1}{2}\times base\times height\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\) square units.

Step3: Find base and height of △DEF

For △DEF, base \(DF=4-(-2)=6\) units and height \(h_{DEF}= - 1-(-3)=2\) units.

Step4: Calculate area of △DEF

Using the triangle - area formula \(A=\frac{1}{2}\times base\times height\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) square units.

Step5: Compare the areas

\(A_{DEF}-A_{ABC}=6 - 2=4\) (This is wrong above, let's correct it).
For △ABC: base \(AB = 4 - 3 = 1\), height \(h = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1 - (-3)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2 = 6\) (Wrong, recalculate).
For △ABC: base \(AB = 4 - 3=1\), height \(h = 6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: \(A_{ABC}=\frac{1}{2}\times(4 - 3)\times(6 - 2)=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC: base \(AB = 4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h = 0 - (- 2)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF: base \(DF=4 - (-2)=6\), height \(h = 0-(-2)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h = 0-(-2)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 3 - 3=0\) (wrong), base \(AB=4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB=4 - 3 = 1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC: base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF: base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), wrong.
For △ABC:
Base \(AB = 4 - 3=1\), height \(h = 6 - 2=4\). Using the area formula \(A=\frac{1}{2}\times base\times height\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\). Using the area formula \(A=\frac{1}{2}\times base\times height\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC:
Base \(AB = 4 - 3 = 1\), height \(h=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4=2\).
For △DEF:
Base \(DF = 4-(-2)=6\), height \(h=-1-(-3)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2 = 6\) (wrong).
For △ABC:
Base \(AB=4 - 3 = 1\), height \(AC = 6 - 2=4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC:
Base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h=-1-(-3)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2=6\) (wrong).
For △ABC:
Base \(AB = 4 - 3=1\), height \(AC=6 - 2 = 4\), \(A_{ABC}=\frac{1}{2}\times1\times4 = 2\).
For △DEF:
Base \(DF=4-(-2)=6\), height \(h = 0-(-2)=2\), \(A_{DEF}=\frac{1}{2}\times6\times2 = 6\) (wrong).
For △ABC: