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Question-93991




Question Number 93991 by i jagooll last updated on 16/May/20
Commented by i jagooll last updated on 16/May/20
find the shaded area
$$\mathrm{find}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area} \\ $$$$ \\ $$
Commented by i jagooll last updated on 16/May/20
anyone help me this question
$$\mathrm{anyone}\:\mathrm{help}\:\mathrm{me}\:\mathrm{this}\:\mathrm{question} \\ $$
Commented by Tony Lin last updated on 16/May/20
8×5×(1/2)×(1/5)+8×5×(1/2)×(1/8)  =4+(5/2)=6(1/2)
$$\mathrm{8}×\mathrm{5}×\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{5}}+\mathrm{8}×\mathrm{5}×\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$=\mathrm{4}+\frac{\mathrm{5}}{\mathrm{2}}=\mathrm{6}\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by Kunal12588 last updated on 16/May/20
sir Tony, your explanation will be appreciated. pls
Commented by i jagooll last updated on 16/May/20
sir Tony how this formula?
$$\mathrm{sir}\:\mathrm{Tony}\:\mathrm{how}\:\mathrm{this}\:\mathrm{formula}? \\ $$
Commented by Tony Lin last updated on 16/May/20
Commented by i jagooll last updated on 16/May/20
next sir? please
$$\mathrm{next}\:\mathrm{sir}?\:\mathrm{please} \\ $$
Commented by Kunal12588 last updated on 16/May/20
8×5 is area of rect., ×1/2 is of triangle but why ×1/5 and ×1/8?
Commented by Tony Lin last updated on 16/May/20
Total area is 8×5=40  areas of green color has bottom side 1,  which account for (1/5) in short side  of the rectangle, and the two triangles  can be thought to be one triangle   with double height  so the area of green side is  (1/2)×((1/5)×40)=4  so do blue parts  (1/2)×((1/8)×40)=(5/2)  but actually  the easier way to do the question  need not calculate the  total area   just (1/2)×(1×8+1×5)=6(1/2)
$${Total}\:{area}\:{is}\:\mathrm{8}×\mathrm{5}=\mathrm{40} \\ $$$${areas}\:{of}\:{green}\:{color}\:{has}\:{bottom}\:{side}\:\mathrm{1}, \\ $$$${which}\:{account}\:{for}\:\frac{\mathrm{1}}{\mathrm{5}}\:{in}\:{short}\:{side} \\ $$$${of}\:{the}\:{rectangle},\:{and}\:{the}\:{two}\:{triangles} \\ $$$${can}\:{be}\:{thought}\:{to}\:{be}\:{one}\:{triangle}\: \\ $$$${with}\:{double}\:{height} \\ $$$${so}\:{the}\:{area}\:{of}\:{green}\:{side}\:{is} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}×\left(\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{40}\right)=\mathrm{4} \\ $$$${so}\:{do}\:{blue}\:{parts} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}×\left(\frac{\mathrm{1}}{\mathrm{8}}×\mathrm{40}\right)=\frac{\mathrm{5}}{\mathrm{2}} \\ $$$${but}\:{actually} \\ $$$${the}\:{easier}\:{way}\:{to}\:{do}\:{the}\:{question} \\ $$$${need}\:{not}\:{calculate}\:{the}\:\:{total}\:{area}\: \\ $$$${just}\:\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{1}×\mathrm{8}+\mathrm{1}×\mathrm{5}\right)=\mathrm{6}\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by Kunal12588 last updated on 16/May/20
thanks sir, and yes second method is much easier, and easy to understand.
Commented by i jagooll last updated on 16/May/20
thank you mr Toni
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{mr}\:\mathrm{Toni} \\ $$
Answered by mr W last updated on 16/May/20
Commented by mr W last updated on 16/May/20
red shaded=2×((1×2.5)/2)=2.5  green shaded=2×((1×4)/2)=4  total shaded=2.5+4=6.5
$${red}\:{shaded}=\mathrm{2}×\frac{\mathrm{1}×\mathrm{2}.\mathrm{5}}{\mathrm{2}}=\mathrm{2}.\mathrm{5} \\ $$$${green}\:{shaded}=\mathrm{2}×\frac{\mathrm{1}×\mathrm{4}}{\mathrm{2}}=\mathrm{4} \\ $$$${total}\:{shaded}=\mathrm{2}.\mathrm{5}+\mathrm{4}=\mathrm{6}.\mathrm{5} \\ $$
Commented by i jagooll last updated on 16/May/20
thank you mr W
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{mr}\:\mathrm{W} \\ $$

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