A square of side 10 has a smaller square of side 4 cut out of one corner. What is the area of the shape that remains?
Text description of the figure
A large square of side 10 with a smaller square of side 4 removed from its top-right corner, leaving an L-shaped region shaded.
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Find the whole, find the hole, subtract.
2The strategy
Do not try to measure the L-shape directly. Work out the area of the big square and the area of the piece removed, then take one from the other.
3The full solution
The big square has area 10 x 10 = 100, the cut-out has area 4 x 4 = 16, so what remains is 100 - 16 = 84.
Solution
The reliable way
The big square has area 10 x 10 = 100. The removed square has area 4 x 4 = 16. The remaining shape has area 100 - 16 = 84. The transferable idea: for a shaded region that is what is left over, find the whole and the hole rather than measuring the odd shape directly.
The elegant way
Cut the L into a 10 by 6 rectangle and a 6 by 4 rectangle: 60 + 24 = 84, which is a useful check on the subtraction.
Why this is on the test: Shaded-region questions reward subtracting rather than measuring, and the wrong answers here come from subtracting the wrong quantity.