IMO Practice Test — Area (Counting Squares)
6 Questions • 10 min • Olympiad level
10:00
Question 1 of 6
hard
A rectangle has area 36 cm². Give two possible pairs of side lengths.
3x12 and 4x9
6x6 and 2x18
All of the above pairs work
Cannot determine
Explanation: 36 cm² can be made by 1x36, 2x18, 3x12, 4x9, 6x6. Multiple pairs work.
Question 2 of 6
hard
A square has the same area as a 4 cm x 9 cm rectangle. What is the square's side?
5 cm
6 cm
7 cm
8 cm
Explanation: Rectangle area = 4x9 = 36 cm². Square side = sqrt(36) = 6 cm.
Question 3 of 6
hard
A rectangle's area is 24 cm². If you double both length and width, what is the new area?
48 cm2
72 cm2
96 cm2
192 cm2
Explanation: If L and W are both doubled: new area = (2L)x(2W) = 4LW = 4x24 = 96 cm².
Question 4 of 6
hard
A rectangle's length is twice its width. Area = 72 cm². Find the dimensions.
6x12 cm
8x9 cm
4x18 cm
3x24 cm
Explanation: Let W = width, L = 2W. L x W = 2W^2 = 72. W^2 = 36. W=6, L=12.
Question 5 of 6
hard
Which has more area: 8 cm x 3 cm or 5 cm x 5 cm?
8x3 = 24 cm2
5x5 = 25 cm2
Equal
Cannot tell
Explanation: 8x3=24 cm². 5x5=25 cm². 25>24, so 5x5 has more area.
Question 6 of 6
hard
How many 2 cm x 3 cm tiles are needed to cover a 6 cm x 8 cm floor?
6
8
12
16
Explanation: Floor area = 6x8=48 cm². Tile area = 2x3=6 cm². Tiles needed = 48/6 = 8. Wait: 48/6=8. Answer is 8.