Question

Find the area of the quadrilaterals, the coordinates of whose vertices are

(1, 2), (6, 2), (5, 3) and (3, 4)

Answer 1

Let the vertices of the quadrilateral be A (1, 2), B (6, 2), C (5, 3), and D (3, 4). Join AC to form two triangles ΔABC and ΔACD.

Area of a triangle `=1/2 {x_1(y_2-y_3)+x_2(y_3-y_1)+(y_1-y_2)}` 

Area of ΔABC `=1/2 {1(2-3)+6(3-2+5(2-2)}`

`=1/2(-1+6)=5/2` square units 

Area of ΔACD `=1/2{1(3-4)+5(4-2)+3(2-3)}`

`=1/2 {-1+10-3}=3`  square   units  

Area of `square`ABCD = Area of ΔABC +Area of ΔACD 

`=(5/2+3)` square units = 11/2 square units