Compute area in split seconds

Algebra Level 2

Find the area of the triangle formed by the axis intercepts of the plane x a + y b + z c = 1 \frac{x}{a}+\frac{y}{b}+\frac{z}{c} = 1

( a 3 b 3 + b 3 c 3 + a 3 c 3 ) 1 3 4 \frac{(a^3b^3+b^3c^3+a^3c^3)^{\frac{1}{3}}}{4} a b + b c + a c 2 \frac{ab+bc+ac}{2} a 2 b 2 + b 2 c 2 + a 2 c 2 2 \frac{\sqrt{a^2b^2+b^2c^2+a^2c^2}}{2} a 2 + b 2 + c 2 4 ∗ a b c \frac{\sqrt{a^2+b^2+c^2}}{4}*\sqrt{abc}

Rakesh Prasad by Rakesh Prasad , 47, India

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1 solution

Connor Kenway
Mar 31, 2014

area of triangle= 1/2*abs(cross product of vectors representing any two sides) just find the vectors representing the sides and then find their cross product using determinant take the absolute value as area is positive and divide by 2.

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