National Trail

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National Trail
Praça do Papa

• Ms.Freire Lucia Helena
• By Alexandre, Gustavo, Jacques e Raphael

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History

• Praça do Papa is located at Belo Horizonte,
  capital of Minas Gerais. Years ago Praça do Papa
  was called Israel Pinheiro, name given by
  Juscelino Kubitschek in homage to his friend.
  Israel Pinheiro was the mayor of Minas Gerais. In
  1980, Pope John Paul II went to visit the city of
  Belo Horizonte. The pope celebrated an outdoor
  mass at the place. Afterwards the public squares
  name changed to
• Praça do Papa.
• Nowadays the place is
• used for shows, celebrations
• and masses. The public
• square is located between
• Rua do Amendoim and Mangabeiras Park. The
  population elected the place an official symbol
  of the city.

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Mathematical Problem

• Problem
• The city hall of Belo Horizonte is organizing a
  show, presenting Caetano Velloso at the Praça do
  Papa. They are trying to get funds for orphanages
  of the city. The City Hall asked us to find the
  area of the place giving us the measurements of
  base1 and base 2 of the stage that is a trapezoid
  and also giving one of the angles in the
  trapezoid. They told us that the perimeter of the
  stage is equal to the diameter of the place that
  has a shape of a circle. They also marked the
  center of the circle for us. We have to know the
  area of the place, how many people can be in the
  show area (considering 1 person per square
  meter), see how much money we can make
  (considering that the price of the ticket is 18
  reais), and inform them of the circumference so
  as to calculate how many meters of gate will we
  need to guarantee security.

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Solving the problem

• We found the base of the right triangle
• We found the hypotenus of the triangle
• We found the perimeter of the trapezoid
• We found the diameter of the circle.
• We found the area and the circumference of the
  circle.

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• We found a triangle, which is a special one(30,
  60, 90).The side opposite to the 30º b,
  opposite to 60º b SQRT 3, and opposite to 90º
  2b. Through this we found the permiter of the
  trapezoid that is equal to the diameter of the
  public square.
• 30m 20m 10m 10m Perimeter of the
  Trapezoid
• 70m Perimeter of the Trapezoid
• 70m Diameter of the Circle

• Circumference ?d
• Circumference 70 3.14
• Circumference 219,8m
• Area ?r²
• Area 3.14 35²
• Area 3846.5m²

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Results

• Circumference 219.8m
• Gate surrounding 220m
•  
• Area 3,846.5m²
• 1 Person 1m²
• Capacity 3,846 people
• 1 ticket R18,00
• Maximum Funds R69.228,00
• Caetano Velloso donation R772,00
• Total money for the Orphanages R70.000,00
•  

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Bibliography

• www.belotur.com.br
• www.google.com.br
• www.cade.com.br
• www.uol.com.br/bhonline/pracas.htm