Kissing Triangles
Determine the total shaded area of the 'kissing triangles'.
Age
11 to 14
Challenge level
Problem
Determine the total area of the two kissing triangles shaded red.
Is there more than one way of drawing the shape?
Image
Is there more than one way of drawing the shape?
Getting Started
Try drawing a diagram of the shape for yourself, making sure it's to scale. See if you can find the area of some parts of the shape first.
You may wish to use GeoGebra to investigate the shape further.
You may wish to use GeoGebra to investigate the shape further.
Student Solutions
The solution is 18 square centimetres and everyone who submitted a response got it right. Of special mention was the work of Sarah at Hethersett High School and Bryony with Sarah from Maidstone Girls' Grammar, all of whom had painstakingly set out their solutions complete with annotations and
diagrams.
Some people managed to spot that it there are multiple ways of drawing the shape; the point in the middle where the triangles 'kiss' can be moved left or right! Well done to those who realised that despite the variety of ways of drawing the shape, the area is always 18 cm2. Brilliant!