Three "regular" triangles

The problem

This problem is connected with my post to geometry-puzzles newsgroup,
from which I present here some text:
Take triangle ABC with all acute angles, with vertices A, B, C and sides a=BC, b=CA, and c=AB, see the Figure: [Graphics:Images/RT-1.jpg]

Do next six easy construction steps:
1A. Draw the circle with center at A , and with radius AD (AD being a height from vertex A to side BC );
1B. draw the circle with center at B , and with radius BE (BE being a height from vertex B to side AC);
1C. draw the circle with center at C , and with radius CF (CF being a height from vertex C to side AB );
2A. find point I (inside the triangle ABC!) of intersection of circles in 1B and 1C;
2B. find point K (inside the triangle ABC!) of intersection of circles in 1A and 1C;
2C. find point L (inside the triangle ABC!) of intersection of circles in 1A and 1B.

For any given triangle ABC with all acute angles, the triangle with vertices I, K, L is unique (and easy to construct).
Also the circular triangle, with the same vertices I, K, L but with sides IFK, KDL, LEI is unique (and easy to construct).

Now assuming that we know side lengths of triangle ABC:
1. Find the area (and perimeter) of the triangle IKL.
2. Find the area (and perimeter) of the circular triangleIFKDLEI.

The hint

First, consider the case of the regular triangle ABC, the case shown in the above Figure.
In this case triangle IKL is also regular and problem is much more easier.

The answer

See here, but better to try yourself!

The Solution

N/A