Question

Find the area of the triangle whose vertices are : (i) (2, 3), (–1, 0), (2, – 4) (ii) (–5, –1), (3, –5), (5, 2)

Answer 1

(i) Area of a triangle is given by

Area of triangle = 1/2 {x₁ (y₂ - y₃)+ x₂ (y₃ - y₁)+ x₃ (y₁ - y₂)}
Area of the given triangle = 1/2 [2 { 0- (-4)} + (-1) {(-4) - (3)} + 2 (3 - 0)]
                                          = 1/2 {8 + 7 + 6}
                                          = 21/2 square units.

(ii) Area of the given triangle = 1/2 [-5 { (-5)- (4)} + 3(2-(-1)) + 5{-1 - (-5)}]
                                                = 1/2{35 + 9 + 20}
                                                = 32 square units