Difficulty: Tricky

Green triangle and hexagon on a yellow background.

Which shape will give Imogen’s goats more area?

Imogen has had enough of her goats getting into her veggie patch. She’s bought wire and poles, but before she starts building, she must work out what shape fence she needs.

The two options she’s tossing up are either an equilateral triangle with two metre sides, or a regular hexagon with one metre sides. Either way, the perimeter will be the same: six metres.

Imogen wants the option with more area inside. Can you help her work out which option that is?


Scroll down or click for a hint, or the answer!

brain icon


Brainteaser hint

It’s tricky to work out the area inside a hexagon – can you cut it into triangles?

brain icon


Brainteaser answer

Triangel and hexagon with pink lines dividing them into triangles.

Since the hexagon fence contains more one metre triangles, it has the bigger area!

Let’s start with a bit of intuition. Round shapes are better at holding big areas than spiky ones – that’s why bubbles are round. A regular hexagon is rounder than a triangle, so it’s probably going to have more area inside. But to prove it, you’ll need to use maths.

Hexagons and triangles are different shapes, which makes them hard to compare. Luckily, you can turn the hexagon into equilateral triangles quite easily. If you connect opposite corners, it’s like six pizza slices, each an equilateral triangle with one metre sides.

How about the triangular fence? Each of its sides are two metres long, so cut it into one metre triangles. Find the midpoint of each side and connect them, cutting the big triangle into four triangles, each with one metre sides.

Since the hexagon fence contains more one metre triangles, it has the bigger area!

Also in this newsletter:

Magnifying sound
Bugs are back, but where have they been?
Still alive – a quick quiz

For more brainteasers and puzzles for kids, subscribe to Double Helix magazine!

Subscribe now! button

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

By submitting this form, you give CSIRO permission to publish your comments on our websites. Please make sure the comments are your own. For more information please see our terms and conditions.

Why choose the Double Helix magazine for your students?

Perfect for ages 8 – 14

Developed by experienced editors

Engaging and motivating

*84% of readers are more interested in science

Engaging students voice