Question

The area of the pentagon formed by the vertices $(1,2),(4,1),(5,3),(3,7),(2,6)$ is

• A. $32\text{sq. units}$
• B. $16\text{sq. units}$
• C. $14\text{sq. units}$
• D. $28\text{sq. units}$

Answer 1

The correct option is C $14\text{sq. units}$

Given vertices of the pentagon are $(1,2),(4,1),(5,3),(3,7),(2,6)$
We know that, the area of pentagon
$\Delta =\frac{1}{2}\left|\begin{array}{cccccc}{x}_1& x_2& x_3& x_4& x_5& x_1\\ y_1& y_2& y_3& y_4& y_5& y_1\end{array}\right|\Rightarrow \Delta =\frac{1}{2}\left|\begin{array}{cccccc}1& 4& 5& 3& 2& 1\\ 2& 1& 3& 7& 6& 2\end{array}\right|\Rightarrow \Delta =\frac{1}{2}|(1-8)+(12-5)+(35-9)+(18-14)+(4-6)|\Rightarrow \Delta =\frac{1}{2}|-7+7+26+4-2|\therefore \Delta =14\text{sq. units}$