Question

The area of ∆ABC with vertices A(3, 0), B(7, 0) and C(8, 4) is

(a) 14 sq units
(b) 28 sq units
(c) 8 sq units
(d) 6 sq units

Answer 1

(c) 8 sq units
The given points are $A\left(3,0\right),B\left(7,0\right)\text{and}C\left(8,4\right)$.
Here, $\left(x_1=3,y_1=0\right),\left(x_2=7,y_2=0\right)\text{and}\left(x_3=8,y_3=4\right)$
Therefore,
$\text{Area of}∆ABC=\frac{1}{2}\left[x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right]$

$$\begin{gathered} =\frac{1}{2}\left[3\left(0-4\right)+7\left(4-0\right)+8\left(0-0\right)\right] \\ =\frac{1}{2}\left[-12+28+0\right] \\ =\left(\frac{1}{2}\times 16\right) \\ =8\text{sq units} \end{gathered}$$