devarshi-dt-logo

Question:

In fig., the area of triangle ABC (in sq. units) is:

10

7.5

15

2.5

Solution:

Given: Coordinates of Point A(1,3), B(−1,0) and C(4,0)
Construction: Drop a perpendicular from A on x-axis, which meets x-axis at D≡(1,0)
Now in ΔADC, AD=3, DC=3
Area of ΔADC = 1/2 × DC × AD = 1/2 × 3 × 3 = 9/2 cm²
Now in ΔADB, AD=3, DB=2
Area of ΔADB = 1/2 × DB × AD = 1/2 × 2 × 3 = 3 cm²
Area of ΔABC = Area of ΔADC + Area of ΔABD = 9/2 + 3 = 15/2 = 7.5 cm²