The area of the pentagon whose vertices are (4, 1), (3, 6),... | MATH - POINTS RELATE TO TRIANGLE (ORTHOCENTRE,...) | SolveeIt | Solveeit

Today, August 18

Question

The area of the pentagon whose vertices are

(4, 1), (3, 6), (– 5,1), (– 3, –3) and (–3, 0) is-

A

30 sq. units

B

45 sq. units

C

60 sq. units

D

None of these

Answer

30 sq. units

Explanation

Solution

Area = $\frac{1}{2}\left\lbrack \begin{matrix} 4 & 1 \ 3 & 6 \end{matrix} + \begin{matrix} 3 & 6 \

5 & 1 \end{matrix} + \begin{matrix}
5 & 1 \
3 & - 3 \end{matrix} + \begin{matrix}
3 & - 3 \
3 & 0 \end{matrix} + \begin{matrix}
3 & 0 \ 4 & 1 \end{matrix} \right\rbrack$

= $\frac{1}{2}$ [24– 3 + 3 + 30 + 15 +3 – 9 – 3 ]

= 30 units²