Question

in the adjoining figure ABCD is a shaded rectangle. find the area of the shaded region

Answer 1

Hii !!



ABCD is a rectangle, in which


AD = 12 cm, DF = 10 cm , BE = 7 cm and AB = 18 cm.




As we know that opposite sides are always equal.


So,



AD = BC = 12 cm and AB = DC = 18 cm.




Length of rectangle = 18 cm

And,

Breadth of rectangle = 12 cm


Therefore,


Area of rectangle = L × B = 18 × 12 = 216 cm².


BC = 12 cm and BE = 7 cm


Therefore,


EC = BC - BE = 12 - 7 =5 cm.


And,



DC = 18 cm , DF = 10 cm


Therefore,


FC = DC - DD = 18 - 10 = 8 cm.






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As we can see that ∆ ADF , ∆ECF , ∆ABE are right angled triangle .





Therefore,



Area of ∆ADF = 1/2 × AD × DF


Area of ∆ADF = 1/2 × 12 × 10 = 60 cm²





Area of ∆ECF = 1 /2 × EC × FC




Area of ∆ ECF = 1/2 × 8 × 5 = 20 cm².




And,


Area of ∆ABE = 1/2 × AB × BE


Area of ∆ ABE = 1/2 × 18 × 7 = 56 cm².



Therefore,


Area of the shared region = Area of rectangle - (area of ∆ ADF + area of ∆ ECF + Area of ∆ ABE )



=> [ 216 - ( 60 + 20 + 56 ) ] cm².



=> [ 216 - ( 136 ) ] cm².



=> ( 216 - 136 ) cm².



=> 80 cm².

Answer 2

Answer:

do it yourself i will help you

down with the steps

Step-by-step explanation:

area of rectangle - the area of three unshaded triangles

a:l*b-1/2*b*h*1/2*b*h*1/2*b*h