Question

find the area of the polygon with the given vertices. e(3, 1), f(3, - 2), g(- 2, - 2)
the area is square units.

Explanation:

Step1: Determine the shape

The polygon with vertices $E(3,1), F(3, - 2), G(-2,-2)$ is a right - triangle. The distance between $E(3,1)$ and $F(3,-2)$ is vertical and the distance between $F(3,-2)$ and $G(-2,-2)$ is horizontal.

Step2: Calculate the base length

The base of the right - triangle is the horizontal distance between $F(3,-2)$ and $G(-2,-2)$. Using the distance formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, for points with the same $y$ - value ($y=-2$ here), the distance $FG=\vert3-(-2)\vert=\vert3 + 2\vert = 5$.

Step3: Calculate the height length

The height of the right - triangle is the vertical distance between $E(3,1)$ and $F(3,-2)$. For points with the same $x$ - value ($x = 3$ here), the distance $EF=\vert1-(-2)\vert=\vert1 + 2\vert=3$.

Step4: Calculate the area

The area formula for a triangle is $A=\frac{1}{2}bh$. Substituting $b = 5$ and $h = 3$ into the formula, we get $A=\frac{1}{2}\times5\times3=\frac{15}{2}=7.5$.

Answer:

$7.5$