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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?

- 9
- 15
- 17

Geometry

Area

Square

But try the problem first...

Answer:15

Source

Suggested Reading

AMC-8, 2015 problem 25

Challenges and Thrills of Pre College Mathematics

First hint

Find the Length of HG......

Can you now finish the problem ..........

Second Hint

Draw the big square in the remaining space of the big sqare and find it's area .......

can you finish the problem........

Final Step

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.

- https://www.cheenta.com/area-of-a-triangle-amc-8-2018-problem-20/
- https://www.youtube.com/watch?v=W9XdZd8zXPA

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