Question

The area of triangle with vertices $A(5,0),B(8,0)$ and $C(9,5)$ is

• A. $7\frac{1}{4}$
• B. $7\frac{1}{2}$
• C. $\frac{15}{4}$
• D. None of the above

Answer 1

Answer: (B)

$7\frac{1}{2}$

Area of triangle $=\frac{1}{2}\left[\begin{array}{c}{x}_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\end{array}\right]$

$A=\frac{1}{2}\left[\begin{array}{c}5(0-5)+8(5-0)+9(0-0)\end{array}\right]$

$A=\frac{1}{2}\left[\begin{array}{c}-25+40\end{array}\right]=\frac{15}{2}$ square units.

So, option B is correct.