Mathematics
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OpenStudy (aizhalee):
(Fan and Medal will be given)!
Help with Area
Find the area of the image below:
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OpenStudy (aizhalee):
OpenStudy (michele_laino):
hint:
the area of your geometrical shape, is given by the sum of the areas of these triangles:
OpenStudy (aizhalee):
so what exactly do I do ? Im not too well with this benchmark D: .
OpenStudy (michele_laino):
we have: area of triangle ABE:
\[A = \frac{{BE \times AK}}{2} = \frac{{8 \times 5}}{2} = ...\]
OpenStudy (aizhalee):
so 8 * 5 = 40 an d 40 divided by 2 is 20 .
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OpenStudy (michele_laino):
ok!
OpenStudy (michele_laino):
area of triangle CDE:
\[A = \frac{{CE \times DK}}{2} = \frac{{5 \times 4}}{2} = ...\]
OpenStudy (aizhalee):
5 * 4 equals 20 and 20 divded by 2 is 10
OpenStudy (michele_laino):
ok!
OpenStudy (michele_laino):
finally:
area of triangle CBE:
\[A = \frac{{BE \times CE}}{2} = \frac{{8 \times 5}}{2} = ...\]
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OpenStudy (aizhalee):
8*5 equals 40 again divided by two is 20 :D
OpenStudy (michele_laino):
ok!
OpenStudy (michele_laino):
so total area is:
20+10+20=...
OpenStudy (aizhalee):
50
OpenStudy (michele_laino):
yes!
nevertheless that answer is not an option of yours
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OpenStudy (aizhalee):
wow , :/
OpenStudy (michele_laino):
my reasoning is right, I don't understand
maybe is there a scale factor, for your drawing?
OpenStudy (michele_laino):
namely, how many units are the area of the littlest square, of your drawing?
OpenStudy (aizhalee):
can u help me find the perimeter for it please michele , D: its not area , its perimeter. sorry ive made a mistake
OpenStudy (michele_laino):
ok!
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OpenStudy (michele_laino):
then we have to apply the theorem of Pitagora repeatedly
OpenStudy (michele_laino):
so we can write this:
\[BC = \sqrt {C{E^2} + B{E^2}} = \sqrt {{5^2} + {8^2}} = \sqrt {25 + 64} = ...?\]
OpenStudy (aizhalee):
ok is that is 89
OpenStudy (michele_laino):
yes! and what is:sqrt(89)=...?
OpenStudy (aizhalee):
9.433
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OpenStudy (michele_laino):
that's right!
OpenStudy (michele_laino):
now we have:
\[AB = \sqrt {A{H^2} + B{H^2}} = \sqrt {{5^2} + {6^2}} = \sqrt {25 + 36} = ...?\]
OpenStudy (michele_laino):
OpenStudy (aizhalee):
its 61
OpenStudy (michele_laino):
and what is:
sqrt(61)=...?
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OpenStudy (aizhalee):
the square root of 61is 7.81
OpenStudy (michele_laino):
perfect!
OpenStudy (aizhalee):
:D
OpenStudy (michele_laino):
now we have:
\[AE = \sqrt {A{H^2} + E{H^2}} = \sqrt {{5^2} + {2^2}} = \sqrt {25 + 4} = ...?\]
OpenStudy (aizhalee):
25 plus 4 is 29 and the square root of 29 is 5.38
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OpenStudy (michele_laino):
yes! correct!
OpenStudy (michele_laino):
next we have:
\[ED = \sqrt {K{D^2} + E{K^2}} = \sqrt {{4^2} + {2^2}} = \sqrt {16 + 4} = ...?\]
OpenStudy (aizhalee):
16 + 4 = 20 and square root of 20 is 4.47
OpenStudy (michele_laino):
ok!
OpenStudy (michele_laino):
finally, we have:
\[CD = \sqrt {K{D^2} + C{K^2}} = \sqrt {{4^2} + {3^2}} = \sqrt {16 + 9} = ...?\]
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OpenStudy (aizhalee):
5 :D
OpenStudy (michele_laino):
perfect!
OpenStudy (michele_laino):
so the requested perimeter, is:
BC+AB+AE+ED+CD=
=9.43+7.81+5.39+4.47+5=...?
OpenStudy (aizhalee):
32.1 :D yipee
OpenStudy (michele_laino):
that's right! :)
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OpenStudy (aizhalee):
Thank you sooo much :D i will be adding these into my notes thanks a lot I appreciate it ! God bless.
OpenStudy (michele_laino):
Thanks!! :) :)
OpenStudy (aizhalee):
Yw :)
OpenStudy (michele_laino):
:)