Question

graph △fgh with vertices f(-4, 5), g(-7, 5), and h(-7, 0). what is the area of △fgh? area = square units

Explanation:

Step1: Find the base length

The points $F(-4,5)$ and $G(-7,5)$ have the same $y -$coordinate. The length of the base $FG$ is found using the distance formula for two points with the same $y -$value, which is $|x_1 - x_2|$. Here, $FG=|-4-(-7)|=3$.

Step2: Find the height length

The points $G(-7,5)$ and $H(-7,0)$ have the same $x -$coordinate. The length of the height (perpendicular to the base) is found using the distance formula for two points with the same $x -$value, which is $|y_1 - y_2|$. Here, the height from $G$ to $H$ is $|5 - 0|=5$.

Step3: Calculate the area of the triangle

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. Substitute the base $b = 3$ and height $h = 5$ into the formula: $A=\frac{1}{2}\times3\times5=\frac{15}{2}=7.5$.

Answer:

$7.5$