A regular polygon with 12 sides (dodecagon) is inscribed in a square of area 24 square units as shown in the figure where four of the vertices are mid points of the sides of the square . The area of the dodecagon in square units is. ans-19.26

• please provide correct solution
• 5 years agoHelpfull: Yes(4) No(0)
• Given that the polygon is inscribed inside a square, we can get the sides of the square.
  Area = 24 square units.
  Side = √24 = 4.899 units
  Given that the four vertices of the polygon are the midpoint of the sides, the polygon is divided into four right-angled triangles whose height and base are equal.
  The height of each triangle is half the sides of the square.
  Therefore:
  h = b = 4.899/2
  = 2.449
  Area of one right angled triangle:
  0.5 × 2.449 × 2.449 = 2.9988 square units.
  We have four right-angled triangles in the polygon hence the area of the polygon is:
  2.9988 × 4 = 11.995 square units
• 6 years agoHelpfull: Yes(3) No(15)
• Given that the the polygon is inscribed inside a square, we can get the sides of the square.
  
  Area = 24 square units.
  
  Side = √24 = 4.899 units
  
  Given that the four vertices of the polygon are the midpoint of the sides, the polygon is divided into four right angled triangle whose height and base are equal.
  
  The height of each triangle is half the sides of the square.
  
  Therefore :
  
  h = b = 4.899/2
  
  = 2.449
  
  Area of one right angled triangle :
  
  0.5 × 2.449 × 2.449 = 2.9988 square units.
  
  We have four right angled triangles in the polygon hence the area of the polygon is :
  
  2.9988 × 4 = 11.995 square units
• 5 years agoHelpfull: Yes(2) No(9)