Question

triangles: area example
a (5,8)
a = \frac{1}{2}bh
c(3,2)
b(9,2)
in the figure above, the vertices of \triangle abc have (x,y) coordinates (5,8), (9,2), and (3,2), respectively. what is the area of \triangle abc?
a 10
b 18.2
c 18.7
d 34

Explanation:

Step1: Identify base length

The points $B(9,2)$ and $C(3,2)$ have the same $y -$coordinate. The length of the base $b$ is the difference in their $x -$coordinates. So $b=\vert9 - 3\vert=6$.

Step2: Identify height

The height $h$ of the triangle is the vertical distance from the point $A(5,8)$ to the line containing $BC$ (where $y = 2$). So $h=\vert8 - 2\vert=6$.

Step3: Calculate area

Use the formula $A=\frac{1}{2}bh$. Substitute $b = 6$ and $h=6$ into the formula: $A=\frac{1}{2}\times6\times6 = 18$.

Answer:

The area of $\triangle ABC$ is 18. Since there is no 18 in the options you provided, there may be a mis - typing in the options or in the problem - solving process check. But the correct area value calculated using the formula $A=\frac{1}{2}bh$ for the given coordinates is 18.