Back to Math Problems (Ages 10 to 11)
The city is planning a large outdoor yoga event in various parks. They need to ensure participants are properly spaced for social distancing.
a) Rectangle Park is 80 m long and 60 m wide. If each participant needs a 3 m by 3 m square, how many people can participate in the yoga event in this park?
b) Circle Park is perfectly round with a diameter of 100 m. If participants need the same 3 m by 3 m squares, approximately how many people can join the yoga event here? (Use 3.14 for π)
c) Triangle Park is an equilateral triangle with sides measuring 120 m each. If the same 3 m by 3 m squares are used, about how many people can participate in the yoga event in this park? (Use 0.433 for √3/4)
d) The city wants to host 1000 participants. If they use Square Park, which is exactly 1 hectare (100 m x 100 m), what is the maximum size of a square that each participant can have while still fitting all 1000 people?
a) For Rectangle Park:
– Length: 80 m ÷ 3 m = 26 full squares along the length
– Width: 60 m ÷ 3 m = 20 full squares along the width
– Total squares: 26 × 20 = 520 people can participate
b) For Circle Park:
– Area of the park: πr² = 3.14 × (50 m)² = 7,850 m²
– Area needed per person: 3 m × 3 m = 9 m²
– Approximate number of people: 7,850 m² ÷ 9 m² ≈ 872 people can participate
c) For Triangle Park:
– Area of an equilateral triangle: (side² × √3) ÷ 4
– Area = (120 m)² × 0.433 = 6,235.2 m²
– Area needed per person: 3 m × 3 m = 9 m²
– Approximate number of people: 6,235.2 m² ÷ 9 m² ≈ 693 people can participate
d) For Square Park:
– Total area: 100 m × 100 m = 10,000 m²
– Area per person: 10,000 m² ÷ 1000 people = 10 m² per person
– Side length of each square: √10 m² ≈ 3.16 m
Each participant can have a square with sides measuring approximately 3.16 m.
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