Question

graph △fgh with vertices f(10, 9), g(-3, 9), and h(10, -2). what is the area of △fgh? area = square units

Explanation:

Step1: Find the base length

The points $F(10,9)$ and $G(-3,9)$ have the same $y$ - coordinate. The distance between two points $(x_1,y)$ and $(x_2,y)$ is given by $d = |x_1 - x_2|$. So the base length $FG$ is $|10-(-3)|=|10 + 3|=13$.

Step2: Find the height

The points $F(10,9)$ and $H(10,-2)$ have the same $x$ - coordinate. The height of the triangle (the perpendicular distance from the vertex opposite the base to the base) is the distance between $(10,9)$ and $(10,-2)$. Using the distance formula for two points $(x,y_1)$ and $(x,y_2)$ which is $d=|y_1 - y_2|$, the height is $|9-(-2)|=|9 + 2| = 11$.

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 base $b = 13$ and height $h = 11$ into the formula, we get $A=\frac{1}{2}\times13\times11=\frac{143}{2}=71.5$.

Answer:

$71.5$