# Find the area of the traingle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1). - Mathematics and Statistics

Sum

Find the area of the traingle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).

#### Solution

Let A = (1, 1, 0), B = (1, 0, 1), C = (0, 1, 1)

l(AB) = sqrt((1 - 1)^2 + (1 - 0)^2 + (0 - 1)^2) = sqrt(0 + 1 + 1) = sqrt2

l(BC) = sqrt((1 - 0)^2 + (0 - 1)^2 + (1 - 1)^2) = sqrt(1 + 1 + 0) = sqrt1

l(CA) = sqrt((0 - 1)^2 + (1 - 1)^2 + (1 - 0)^2) = sqrt(1 + 0 + 1) = sqrt2

∴ l(AB) = l(BC) = l(CA)

∴ the triangle is equilateral

∴ its area = sqrt3/4 ("side")^2

= sqrt3/4 (sqrt2)^2

= sqrt3/2sq units.

Concept: Vectors and Their Types
Is there an error in this question or solution?