Find the area of the quadrilateral whose vertices are $A (1, 1), B (7, - 3), C (12, 2)$ and $D (7, 21)$

123

square units

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132

square units

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142

square units

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256

square units

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Solution

The correct option is B $132$ square units
Area of quadrilateral $A B C D$ is
$\frac{1}{2} [∣ ∣ ∣ \begin{matrix} 1 & 1 7 & - 3 \end{matrix} ∣ ∣ ∣ + ∣ ∣ ∣ \begin{matrix} 7 & - 3 12 & 2 \end{matrix} ∣ ∣ ∣ + ∣ ∣ ∣ \begin{matrix} 12 & 2 7 & 21 \end{matrix} ∣ ∣ ∣ + ∣ ∣ ∣ \begin{matrix} 7 & 21 1 & 1 \end{matrix} ∣ ∣ ∣] = \frac{1}{2} [- 3 - 7 + 14 + 36 + 252 - 14 + 7 - 21] = \frac{264}{2} = 132$

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