The radio telescope

A square contains two triangles. What fraction of the square do they cover?

Scroll down for a solution to this problem.


A fraction of 7/20 of the square is red.

To find a solution, we have to think outside the box. Extending two lines as shown, the upper red triangle is enlarged to one similar to the small triangle. It has a base of 2, so its size is 4 times larger.

Drawing the altitude from top to bottom, we can now fill in the heights. The rest is algebra. The large triangle has area 1/2*2*4/5 – 1/2*2*1/2=3/10. The small one has 1/2*1/2*1/5=1/20.


This puzzle inspired Belladonna to this French poem:

Vous voyez
Des triangles , des carrés
Rouges et verts
Ne vous mettez pas
De frontières
Et vous y verrez
un vitrail de verre
Prêt à orner un lieu de prière
Une noble et belle destinée
D’un chef d’oeuvre par les mains taillées.
Une pièce de toute beauté


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