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: Identify the polygon type

The points form a right - angled triangle. The vertical side length between $E(3,1)$ and $F(3, - 2)$ can be found using the distance formula for points with the same $x$ - coordinate. The horizontal side length between $F(3,-2)$ and $G(-2,-2)$ can be found using the distance formula for points with the same $y$ - coordinate.

Step2: Calculate the vertical side length

For points $E(3,1)$ and $F(3,-2)$ with $x_1 = x_2=3$, the length $EF=\vert y_1 - y_2\vert=\vert1-(-2)\vert = 3$.

Step3: Calculate the horizontal side length

For points $F(3,-2)$ and $G(-2,-2)$ with $y_1 = y_2=-2$, the length $FG=\vert x_1 - x_2\vert=\vert3-(-2)\vert = 5$.

Step4: Calculate the area of the triangle

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. Here, $b = 5$ and $h = 3$. So $A=\frac{1}{2}\times5\times3=\frac{15}{2}=7.5$.

Answer:

$7.5$