mathschallenge.net

Problem

An arrow is formed in a 2 2 square by joining the bottom corners to the midpoint of the top edge and the centre of the square.

Find the area of the arrow.

Solution

Consider the two diagrams below.

The area of the square is 4, so the area of the large triangle is 2 (half of the square) and the area of the small triangle is 1 (quarter of the square).

Hence the area of the arrow is 2 1 = 1 square unit.

What would be the area of a similar arrow, drawn in a 10 10 square?
Can you generalise for an n n square?
What about arrows in general?