InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If P (-5, - 3), Q (-4, -6), R (2,-3) and S (1, 2) are the vertices of a quadrilateral PQRS, find its area. |
|
Answer» Let P(−5,−3); Q(−4,−6); R(2,−3) and S(1,2) be the vertices of quadrilateral PQRS. Area of the quadrilateral PQRS = Area of ∆PQR + Area of ∆PSR Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3) = \(\frac{1}2\) |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| Area of ∆PQR = \(\frac{1}2\) |− 5( − 6 + 3 ) − 4( − 3 + 3 ) + 2( −3 + 6) | = \(\frac{1}2\) |15 + 0 + 6| = \(\frac{21}2\) sq. units Area of ∆PSR = \(\frac{1}2\) | − 5( 2 + 3 ) + 1( − 3 + 3 ) + 2( − 3 − 2) | = \(\frac{1}2\) | − 25 + 0 – 10 | = \(\frac{25}2\) sq. units Area of the quadrilateral PQRS = \(\frac{21}2\)+\(\frac{25}2\) = 28 sq. units ∴Hence, the area of the quadrilateral is 28 sq. units. |
|