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AMO · 2027 · Grades 4-5 · Self-study SET 28 Question 7

AMO

Question 7

Which statement is true? For option D, interpret the two heptagons as joined along one complete side, with no overlap, and count the outer boundary sides.

Choose one option.
  1. If a circle and a regular octagon have the same area, the radius of the circle equals the distance from the centre to a vertex of the octagon.
  2. The difference between the numbers of sides of an octagon and a trapezium is a prime number.
  3. All regular quadrilaterals have sides of equal length.
  4. Four more than the number of sides of a decagon equals the number of sides of the figure formed by joining two identical regular heptagons next to each other.
  5. Only right-angled triangles have area $(\text{base}\times\text{height})\div2$.