Home > #MTBoS, Maths, Starters > A nice little triangle puzzle

## A nice little triangle puzzle

Here is a nice little puzzle I saw from brilliant.org on Facebook.

Have you worked it out yet?

Here’s what I did:

First I drew a diagram (obviously).

And worked out the area of the triangle.

Then the area of each sector.

Leaving a subtraction to finish.

Categories: #MTBoS, Maths, Starters Tags: , ,
1. December 5, 2016 at 7:25 pm

I split the equilateral triangle down the middle making a right angled triangle. Used Pythag to find the missing side (sq root 3) – calculated the area of this and multiplied by 2, to find area of original equil. triangle.
For sectors – each has angle of 60 – place next to each other to make semicircle. Calculate area (pi/2).
Shaded pink is the difference between these (root 3 – pi/2).

• December 5, 2016 at 7:28 pm

Lovely method.

2. December 5, 2016 at 7:26 pm

You seem to have taken a long way around here I reckon. Blue bits is half a unit circle – so radius is irrelevant in formula (180/360), so that’s pi/2, area of equilateral triangle is sqrt(3) (Pythag 1 + x^2 = 4) Just need height because 1/2 base is just 1.

• December 5, 2016 at 7:27 pm

I often do take the long way round!

3. December 5, 2016 at 7:29 pm

Nice puzzle. I like the questions from Brilliant. A lot of them are real thinkers.

• December 5, 2016 at 7:30 pm

Yes, they certainly are. Their Facebook page keeps me sharp! (Although I wasn’t too sharp this morning.)

• December 5, 2016 at 7:32 pm

I don’t think I’ve ever considered my maths skills as anything other than amateur! I think school bashes into us all that ‘good at maths’ means elite genius who only ever gets right answers in the most efficient ways.

• December 5, 2016 at 7:44 pm

Haha. It certainly does in some places.