Can You Find The Shaded Area?

We are given the areas of the 3 equilateral triangles

From Catriona Agg

Here’s another fun geometry puzzle from Catriona Agg. The figure is composed of 3 equilateral triangles with areas 9, 1 and 4, as well as an ‘apex triangle’ drawn by connecting the top of the 3 equilateral triangles.

The challenge for us today is to figure out the area of that. When I first looked at this puzzle, I thought of Heron’s Formula and even the cross product.

But in hindsight, there’s a way more simple and elegant method hiding in plain sight.

So give this problem a go now! And when you are ready, keep reading for the solution.