Find the area of quadrilateral $A B C D$ formed by points $A (- 2, - 2), B (5, 1), C (2, 4)$ and $D (- 1, 5)$ .

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Solution

$\begin{matrix} a r e a o f q u a d r i l a t e r a l A B C D = a r e a o f Δ A B C + a r e a o f Δ A D C a r e a o f Δ A B C = \frac{1}{2} \times [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{2}) + x_{3} (y_{1} - y_{2})] A (x_{1}, y_{1}) = A (- 2, - 2) B (x_{2}, y_{2}) = B (5, 1) C (x_{3}, y_{3}) = C (2, 1) D (x_{4}, y_{4}) = D (- 1, 5) a r e a o f Δ A B V = \frac{1}{2} [- 2 (1 - 1) + 5 (1 - 2) + 2 (- 2 - 1)] \Rightarrow= \frac{1}{2} [0 + 15 - 6] \Rightarrow 4.5 u n i t^{2} s i m i l a r l y a r e a o f Δ A D C \Rightarrow \frac{1}{2} [- 2 (1 - 5) + 2 (5 + 2) + (- 1) (- 2 - 1)] \Rightarrow \frac{1}{2} [8 + 14 + 3] = \frac{25}{2} = 12.5 u n i t^{2} a r e a o f q u a d r i a l t e f r a l \Rightarrow 4.5 + 12.5 \Rightarrow 17 u n i t^{2} \end{matrix}$

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Find the area of quadrilateral ABCD formed by points A(−2,−2),B(5,1),C(2,4) and D(−1,5).

Find the area of quadrilateral $A B C D$ formed by points $A (- 2, - 2), B (5, 1), C (2, 4)$ and $D (- 1, 5)$ .