gabbyalicorn
  • gabbyalicorn
Figure DEFG is equivalent to a trapezoid with a semicircle removed from its upper base. What is the area of figure DEFG?
Mathematics
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SOLVED
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chestercat
  • chestercat
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gabbyalicorn
  • gabbyalicorn
https://www.dropbox.com/s/8gu1yxvuppvea7n/Screenshot%202015-06-16%2023.44.12.png?dl=0
Michele_Laino
  • Michele_Laino
first step: we have to compute the area of trapezoid, which is: \[Area = \frac{{\left( {B + b} \right) \times h}}{2} = \frac{{\left( {14 + 8} \right) \times 5}}{2} = ...c{m^2}\]
gabbyalicorn
  • gabbyalicorn
55

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Michele_Laino
  • Michele_Laino
that's right!
Michele_Laino
  • Michele_Laino
second step: we have to compute the area of the half circle: \[area = \pi \times 4 \times 4 = ...c{m^2}\] please don't multiply by 3.14
gabbyalicorn
  • gabbyalicorn
XD okay
gabbyalicorn
  • gabbyalicorn
i got 16
Michele_Laino
  • Michele_Laino
oops.. the area is: \[area = \frac{{\pi \times 4 \times 4}}{2} = ...c{m^2}\]
gabbyalicorn
  • gabbyalicorn
8
Michele_Laino
  • Michele_Laino
yes! it is 8*pi
gabbyalicorn
  • gabbyalicorn
B? :D
Michele_Laino
  • Michele_Laino
now the requested area is the subtraction between those areas, namely: \[{\text{requested area}} = {\text{area of trapezoid - area of halfcircle}}\]
Michele_Laino
  • Michele_Laino
hint: \[\begin{gathered} {\text{requested area}} = {\text{area of trapezoid - area of halfcircle = }} \hfill \\ {\text{ = }}55 - 8\pi = ... \hfill \\ \end{gathered} \]
gabbyalicorn
  • gabbyalicorn
147.58 i think i didnt do it correctly
Michele_Laino
  • Michele_Laino
no, you don't have to multiply by 3.14, the right option is B as you wrote before
gabbyalicorn
  • gabbyalicorn
but then whhy did u put the pi ;-;
Michele_Laino
  • Michele_Laino
because the area of the half circle is: 8*pi
gabbyalicorn
  • gabbyalicorn
:I kay.
Michele_Laino
  • Michele_Laino
:)
gabbyalicorn
  • gabbyalicorn
Thanks. :)
Michele_Laino
  • Michele_Laino
:)
gabbyalicorn
  • gabbyalicorn
gabbyalicorn
  • gabbyalicorn
lol ^
Michele_Laino
  • Michele_Laino
thanks for your picture! It is a beautiful gift :)
gabbyalicorn
  • gabbyalicorn
LOL. Well this time I didn't make it XDDDD but i'm glad you like it.
Michele_Laino
  • Michele_Laino
:)
gabbyalicorn
  • gabbyalicorn
Now i can sleep :) thank you Z_Z

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