Side of the smaller triangle = 6, and larger triangle is x

Using Pythagoras,

height of smaller triangle = sqrt3 * 3

height of larger triangle = sqrt3 * x/2

OB = 1/3 * height of larger triangle = 1/3 * sqrt3 * x/2

OA = 1/3 * height of smaller triangle = 1/3 * sqrt3 * 3 = sqrt3

OB = OA + AB => x*sqrt3/6 = sqrt3 + sqrt3 => x = 12

Area of the border = Area of larger triangle â€“ area of smalletr triangle = (sqrt3 * 12^2)/4 - (sqrt3 * 6^2)/4 = 27 * sqrt3

Friends ...Couldnâ€™t find a shorter way to do it, looking forward for a smarter response

Attachments

pr_t2_36_195.jpg [ 9.33 KiB | Viewed 732 times ]