Question

The figure below shows a square, each of whose sides is 3 centimetres long. Each side is divided into three equal parts and these points are joined to form an octagon:

What is the perimeter of the octagon?

Answer 1

Given: PQRS is a square.

PQ = QR = RS = SP = 3 cm

Each side of the square PQRS is divided into three equal parts.

Similarly, CD = FE = GH = 1 cm

Now, in ΔAHP, ∠APH = 90° (Angle of a square)

So, by using Pythagoras theorem, we have:

Similarly, BC = DE = FG ≈ 1.41 cm

We know that perimeter of an octagon is equal to the sum of lengths of all its sides.

∴ Perimeter of the octagon ABCDEFGH ≈ (1 + 1.41 + 1 + 1.41 + 1 + 1.41 + 1 + 1.41) cm

= 9.64 cm

Thus, the perimeter of the octagon is approximately equal to 9.64 cm.