## Area Of Arrow

#### 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?

Problem ID: 65 (Feb 2002) Difficulty: 1 Star