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find the area of the shaded region | can you find the area of the orange region

geometry problem with solution


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QUESTION

Q-A triangle is divided by eight parallel lines that are equally spaced from each other.

starting from the top color each alternate region in yellow then color the remaining regions in orange.

if the area of the yellow region is 145

what is the area of the orange region


Q-A triangle is divided by eight parallel lines that are equally spaced from each other. starting from the top color each alternate region in yellow then color the remaining regions in orange. if the area of the yellow region is 145 what is the area of the orange region
what is the area of the orange region

Solution

  • Draw another exact triangle as above, then rotate this triangle at a 180 degree angle (see image below)
  • By adopting this method, it becomes a parallelogram.
  • Now, the total area of yellow region becomes 2 \times 145=290
  • the area of the each yellow stripes \frac {290}{5}=58
  • area \; of \; the \; one \; yellow \; stripes \; =area \; of \; the \; one \; orange \; stripes =58
  • Area of all orange region = 58\times4=232
  • This is the area of both triangles so we have to divide by two
  • Area of orange region = \frac {232}{2}=116
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find the area of the shaded region | can you find the area of the orange region | find the area of the shaded region of a triangle

Area of orange region = \frac {232}{2}=116


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