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If the area of a face of a cuboid is one quarter of the area of each of the other two visible faces, what is the area of these faces?
Age
11 to 14
Challenge level
filled star filled star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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The diagram shows a cuboid in which the area of the shaded face is one quarter of the area of each of the two visible unshaded faces.

The total surface area of the cuboid is $72\text{cm}^2$. What is the area of one of the unshaded faces of the cuboid?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.