Question

an equilateral triangle and a regular hexagon have equal perimeter. if the area of the triangle is 12 dm square then the difference of their areas is ​

Answer 1

Answer:

6d

Step-by-step explanation:

Let a be the area of the triangle (so a = 12d) and p be its perimeter

A hexagon drawn around the triangle has area 2a and perimeter that is (2/√3)p (use Pythagoras' Theorem to get this).  So the hexagon in question is obtained by scaling this hexagon by a factor of √3/2.  But this scales the area by the square of the scale factor, so the area of the hexagon in question is 2a times (√3/2)^2; i.e. its area is 3a/2.

The difference between the areas is then 3a/2 - a = a/2.

When a = 12d, the difference then is a/2 = 6d.