Q. 74.4( 8 Votes )

Find area of the

Answer :

Given vertices of the triangle are (2, 7), (1, 1), (10, 8)

Let the vertices of the triangle be given by (x1, y1), (x2, y2), (x3, y3)


Area of triangle is given by Δ =


Area of triangle = Δ =


Expanding the determinant along Row 1


Δ = 1/2 × [2 × (1 × 1 – 8 × 1) – 7 × (1 × 1 – 10 × 1) + 1 × (8 × 1 – 1 × 10)]


Δ = 1/2 × [2 × (1 – 8) – 7 × (1 – 10) + 1 × (8 – 10)]


Δ = 1/2 × [2 × (-7) – 7 × (-9) + 1 × (-2)] = 1/2 × (-14 + 63 – 2) sq. units


Δ = 1/2 × 47 sq. units = 47/2 sq. units


Δ = 47/2 sq. units = 23.5 sq. units

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