- Problem
- Getting Started
- Solution

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

Challenge Level

Triangles are formed by joining the vertices of a skeletal
cube.
How many different types of triangle are there? How many triangles altogether? |

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.

Copyright © 1997 - 2021. University of Cambridge.
All rights reserved.

NRICH is part of the family of activities in the Millennium Mathematics Project.

NRICH is part of the family of activities in the Millennium Mathematics Project.