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100 Points! Please help with this geometry question! Give an explanation, it could be short or statement reasonings! Thanks!

100 Points Please help with this geometry question Give an explanation it could be short or statement reasonings Thanks class=

Respuesta :

mhanifa

Answer:

  • 168 cm²

Step-by-step explanation:

Refer to attached

Given

  • Area of ΔDCF = 63 cm²

To find

  • Area of ΔABC

Solution

  • Let the area of ABC be A, then
  • A = 1/2bh, where b= AC is the base and h is the height of the triangle

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The triangle DCF can be divided into DEC and DEF as per picture and the area of them is:

Area of ΔDEF

  • 1/2DE*h2

Area of ΔDEC

  • 1/2DE*h1

Since D and E are midpoints of AB and BC:

  • DE = 1/2AC = 1/2b
  • And h1 = 1/2h,
  • h2 = 1/2h1 = 1/2*1/2h = 1/4h

So the area of ΔDCF is:

  • 1/2(1/2bh1) + 1/2(1/2bh2) =
  • 1/2(1/2b*1/2h) + 1/2(1/2b*1/4h) =
  • 1/8bh + 1/16bh =
  • 3/16bh

Since the area of ABC is A = 1/2bh we have:

  • 3/8*1/2bh = 3/8A and
  • 3/8A = 63

Solving for A:

  • A = 63*8/3 = 168 cm²
Ver imagen mhanifa

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