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Mathematics 21 Online
OpenStudy (aizhalee):

(Fan and Medal will be given)! Help with Area Find the area of the image below:

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 .

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: \[A = \frac{{BE \times CE}}{2} = \frac{{8 \times 5}}{2} = ...\]

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

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!

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

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)=...?

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

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: \[CD = \sqrt {K{D^2} + C{K^2}} = \sqrt {{4^2} + {3^2}} = \sqrt {16 + 9} = ...?\]

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! :)

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):

:)

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