Try this beautiful problem from AMC-8-2015 (Geometry) based on area of square.
One-inch Squares are cut from the corners of this 5 inch square.what is the area in square inches of the largest square that can be fitted into the remaining space?
Geometry
Area
Square
Answer:15
AMC-8, 2015 problem 25
Challenges and Thrills of Pre College Mathematics
Find the Length of HG......
Can you now finish the problem ..........
Draw the big square in the remaining space of the big sqare and find it's area .......
can you finish the problem........
We want to find the area of the square. The area of the larger square is composed of the smaller square and the four red triangles. The red triangles have base 3 and height 1 . so the combined area of the four triangles is $ 4 \times \frac {3}{2} $=6.
The area of the smaller square is 9+6=15.
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