IMO Geometry 3

Question 1

Which quadrilateral has exactly one pair of parallel sides?

Accepted Answer

Trapezoid

Answer

A trapezoid (also called a trapezium) has exactly one pair of parallel sides.

Question 2

What is the area of a square with perimeter 24 cm?

Accepted Answer

36 cm²

Answer

Each side = 24 ÷ 4 = 6 cm; Area = 6² = 36 cm².

Question 3

In a circle, what is the longest chord called?

Accepted Answer

Diameter

Answer

The diameter is the longest chord of a circle, passing through the center.

Question 4

A triangle has sides of 5 cm, 5 cm, and 8 cm. What type of triangle is it?

Accepted Answer

Isosceles

Answer

An isosceles triangle has exactly two equal sides, which matches the 5 cm, 5 cm, 8 cm triangle.

Question 5

What is the total surface area of a cube with side 3 cm?

Accepted Answer

54 cm²

Answer

A cube has 6 faces; Total surface area = 6 × side² = 6 × 9 = 54 cm².

IMO - International Mathematics Olympiad Practice Test