In the figure shown, a triangle is divided into nine stripes of equal height each parallel to the same side of the triangle. The shaped stripes have a total area of 135 square units. What is the area of the triangle in square units?

• Complete the parallelogram. Then assume the base of stripe be a and height be b. Total area of parallelogram = 9axb. Area of shaded parallelogram = 5axb=135x2. => axb = 54. Now by substituting the value of axb in total area we get 9x54= total area. We know that area of triangle is half of parallelogram therefore Area of triangle will be 9x54/2= 243 sq units.
• 5 years agoHelpfull: Yes(2) No(0)
• The top stripe (a triangle) will have 1`/9 the height of the original triangle and thus (1/9)^2 = 1/81 the are of the original. The top two stripes form a triangle with a height 2/9 of the original and so an area 4/81 of the original. That mean the second stripe has an area of 4/81 - 1/81 = 3/81 of the original triangle. Working your way down with the same reasoning, successive stripes have areas of 5/81, 7/81, 9/81, . . . , and 17/81 of the original triangle. The sum of every other stripe will be 1/81 + 5/81 + 9/81 + 13/81 + 17/81 = 45/81. So 135/A = 45/81 gives an area of 243 square units.
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• 234 sq.units
• 5 years agoHelpfull: Yes(0) No(1)
• It is given that a triangle is divided into nine stripes of equal height each parallel to the same side of the triangle.
  
  A figure is attached with this answer.
  
  The shape stripes have a total area of 135 square units.
  
  Therefore we combine all these parts together we get complete triangle,
  
  Sum of areas of all these parts is equal to the area of triangle.
  
  Therefore area of triangle = 135 square units
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