Coordinates of points are A(5,0), B(6,5),C(9,12),D(-6,9). Find the area of the quadrilateral ABCD.Draw the diagonal AC and find the area of both the triangles so obtained.

Asked by aahnik.mohanty | 31st Dec, 2017, 12:52: PM

Expert Answer:

begin mathsize 16px style Area space of space triangle ABC equals 1 half open vertical bar 5 left parenthesis 5 minus 12 right parenthesis plus 6 left parenthesis 12 minus 0 right parenthesis plus 9 left parenthesis 0 minus 5 right parenthesis close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half open vertical bar 5 cross times left parenthesis negative 7 right parenthesis plus 6 cross times 12 plus 9 cross times left parenthesis negative 5 right parenthesis close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half open vertical bar negative 35 plus 72 minus 45 close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half open vertical bar negative 35 plus 72 minus 45 close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 4 space sq. space units

Area space of space triangle ACD equals 1 half open vertical bar 5 left parenthesis 12 minus 9 right parenthesis plus 9 left parenthesis 9 minus 0 right parenthesis minus 6 left parenthesis 0 minus 12 right parenthesis close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half open vertical bar 5 cross times 3 plus 9 cross times 9 minus 6 cross times left parenthesis negative 12 right parenthesis close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half open vertical bar 15 plus 81 plus 72 close vertical bar
space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 84 space sq. space units
therefore space Area space of space quadrilateral space ABCD equals Area space of space triangle ABC plus Area space of space triangle ACD equals 4 plus 84 equals 88 space sq. space units end style

Answered by Rashmi Khot | 1st Jan, 2018, 09:39: AM