Soma surface
What is the surface area of the solid shown?
Age
11 to 14
Challenge level
Problem
Image
What is the total surface area of the solid?
If you liked this probelm, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Image
You could consider the surface area looking at the shape from each direction.
The shape looks like one of the two shapes on the right from each of the six directions, so the surface area is $ 6 \times 3 \text{cm}^2 = 18\text{cm}^2$.
Alternatively, 3 of the cubes have 5 of their faces showing, whilst the cube in the corner has 3 of its faces showing.
This means a total of $3 \times 5 + 3 = 18$ faces are showing, so the total surface area is $18\text{cm}^2$.