Class 10

Math

All topics

Coordinate Geometry

Find the area of quadrilateral ABCD whose vertices are $A(−3,−1),B(−2,−4),C(4,−1)$ and $D(3,4)$.

Given: ABCD is a quadrilateral whose vertices are $A(−3,−1),B(−2,−4),C(4,−1)$ and $D(3,4)$.

By joining AC, we get two triangles ABC and ADC

We know that:

Area of $ΔABC=21 [x_{1}(y_{2}−y_{3})+x_{2}(y_{3}−y_{1})+x_{3}(y_{1}−y_{2})]$

Area of triangle ABC:

$=21 [−3(−4+1)+(−2)(−1+1)+4(−1+4)]$

$=21 [−3(−5)+(−2)×0+4×3]$

$=21 [15−0+12]=21 ×27=227 $ sq. units

Area of triangle ADC.

$=21 [−3(−4)+4(4+1)+(3)(−1+1)]$

$=21 [−3(−3)+4×5+3×(0)]$

$=21 [9+20−0]=21 ×29=229 $ sq. units.

Now, Area of quadrilateral PQRS$=$Area of triangle ABC$+$ Area of triangle ADC

$=27/2+29/2$

$=28$ sq. units.