Math

Calculate the area of the triangle ABC with vertices A(2,3), B(1-6), C(0,3).

Expert Answers

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The triangle has vertexes A(2,3), B(1, -6), C(0,3)

AB = sqrt( 1 + 81) = sqrt 82

BC = sqrt(1 + 81) = sqrt 82

AC = 2

The area of a triangle is given by the Heron's formula as sqrt [s(s - a)(s - b)(s - c)] where a, b and c are the sides and s is the semi-perimeter.

s = sqrt 82 + 1

sqrt [s(s - a)(s - b)(s - c)]

=> sqrt [(sqrt 82 + 1)(1)(1)( sqrt 82 - 1)]

=> sqrt [ (82 - 1)]

=> 9

The area of the triangle is 9 square units.

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