Question

the graph shows the vertices of a triangle. determine the area of the triangle. enter the unknown segment length(s), then calculate the area of the polygon. area of the triangle: square units

Explanation:

Step1: Find the base length

The base of the triangle is the distance between points $A(- 12, - 1)$ and $W(12,-1)$. Using the distance formula for two - points on a horizontal line (since the $y$ - coordinates are the same), the length of the base $b$ is $|12-(-12)|=24$.

Step2: Find the height

The height $h$ of the triangle is the perpendicular distance from the vertex $R(-1,-8)$ to the line segment $AW$. The $y$ - coordinate of points on $AW$ is $y = - 1$, and the $y$ - coordinate of $R$ is $y=-8$. So the height $h=|-1-(-8)| = 7$.

Step3: Calculate the area

The area of a triangle is given by the formula $A=\frac{1}{2}bh$. Substitute $b = 24$ and $h = 7$ into the formula: $A=\frac{1}{2}\times24\times7=84$.

Answer:

84