Find the area of quadrilateral formed by joining the points (- 4, 2), (- 1, 0), (4, 1) and (2, 5):

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21 .5

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Solution

The correct option is D 21 .5
$1^{s t}$ method: - The simplest way to find this is to put a rectangle around the given quadrilateral and then subtract off the areas of the right triangles that surround it. (See Figure) The area of the entire rectangle is 40, but after subtracting the areas of the 4 right triangles, whose areas are $\frac{5}{2}$ , 4, 9 and 3. we are left with an area of 21.5.

$2^{n d}$ method: - Area of quadrilateral = $2 (x_{1} y_{2} - x_{2} y_{1}) + (x_{2} y_{3} - x_{3} y_{2}) + (x_{3} y_{4} - x_{4} y_{3}) + (x_{4} y_{1} - x_{1} y_{4})$

= $\frac{1}{2} (- 4 \times 0 - (- 1) \times 2) + (- 1 \times 1 - 4 \times 0) + (4 \times 5 - 2 \times 1) + (2 \times 2 - (- 4) \times 5) = 21.5$

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