The side of a regular octagon is half the side of a regular quadrilateral (square). If the perimeter of the quadrilateral is 20cm, what is the perimeter of the octagon?

Correct — B. Work from the square to the octagon.

Square side = perimeter ÷ 4 = 20 ÷ 4 = 5 cm
Octagon side = half of 5 = 2.5 cm

Octagon perimeter = 8 sides × 2.5 = 20 cm → option (b)

Why the others are wrong

• (a)
  10 cm — 10 cm is 4 × 2.5, counting only four sides of the octagon. A regular octagon has eight equal sides.
• (c)
  30 cm — 30 cm needs an octagon side of 30 ÷ 8 = 3.75 cm. The side is half of 5, which is 2.5 cm.
• (d)
  40 cm — 40 cm is 8 × 5: it gives the octagon the square's side and skips the halving.

The perimeter of a regular polygon is number of sides × side length.

The octagon has twice as many sides as the square, each half as long. The two changes cancel, so the perimeters are equal.

Seeing that saves the arithmetic: doubling the count and halving the side leaves the product unchanged.

Key facts

• Perimeter of a regular n-sided polygon = n × side.
• A regular octagon has 8 equal sides and a square has 4.
• Each interior angle of a regular octagon is (8 − 2) × 180° ÷ 8 = 135°.

Common traps

• Giving the octagon the square's side (5 cm), which makes the perimeter 40 cm.
• Multiplying the octagon's side by 4 out of habit from the square.

No directly related past PYQ was found.