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Find the area of quadrilateral PQRS whose vertices are P(-5, -

Question

Find the area of quadrilateral PQRS whose vertices are $P (- 5, - 3), Q (- 4, - 6), R (2, - 3)$ and $S (1, 2)$ .

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Find the area of quadrilateral PQRS whose vertices are

P (- 5, - 3), Q (- 4, - 6), R (2, - 3)

and

S (1, 2)

9 mins ago

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9 mins ago

Text solutionVerified

Given: PQRS is a quadrilateral whose vertices are

P (- 5, - 3), Q (- 4, - 6), R (2, - 3)

and

S (1, 2)

Construction: Join PR

We know that:

Area of

Δ A BC = \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]

Area of triange POR:

= \frac{1}{2} [- 5 (- 6 + 3) + (- 4) (- 3 + 3) + 2 (- 3 + 6)]

= \frac{1}{2} [- 5 (- 3) + (- 4) (0) + 2 (3)]

= \frac{1}{2} [15 + 0 + 6] = \frac{21}{2}

sq. units

Area of triangle PSR.

= \frac{1}{2} [- 5 (- 3 - 2) + 2 (2 + 3) + 1 (- 3 + 3)]

= \frac{1}{2} [- 5 (- 5) + 2 \times 5 + 1 \times 0]

= \frac{1}{2} [25 + 10 + 0] = \frac{35}{2}

sq. units.

Now, Area of quadrilateral PQRS

=

Area of triangle PQR

+

Area of triangle PSR

= 21/2 + 35/2

= 28

sq. units.

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Question Text	Find the area of quadrilateral PQRS whose vertices are $P (- 5, - 3), Q (- 4, - 6), R (2, - 3)$ and $S (1, 2)$ .
Answer Type	Text solution:1
Upvotes	150