Question

find the area of the polygon with the given vertices. j(-3, 4), k(4, 4), l(3, -3) the area is square units.

Explanation:

Step1: Find the length of base

The points $J(-3,4)$ and $K(4,4)$ have the same $y -$coordinate. The length of the base $JK$ is found using the distance formula for points on a horizontal line $d=\vert x_2 - x_1\vert$. Here, $x_1=-3$ and $x_2 = 4$, so $JK=\vert4-(-3)\vert=7$.

Step2: Find the height

The height is the perpendicular distance from the point $L(3,-3)$ to the line $y = 4$. It is calculated as the absolute - value of the difference in the $y -$coordinates, $h=\vert4-(-3)\vert = 7$.

Step3: Calculate the area of the triangle

The area of a triangle is given by the formula $A=\frac{1}{2}\times base\times height$. Substituting the values of base $b = 7$ and height $h = 7$ into the formula, we get $A=\frac{1}{2}\times7\times7=\frac{49}{2}=24.5$.

Answer:

$24.5$