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.
• 4 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.
• 4 years agoHelpfull: Yes(1) No(0)
• 234 sq.units
• 4 years agoHelpfull: Yes(0) No(1)