Question

solve this...........

Answer 1

Hii !!



It seems something is wrong in the question.



DC = 100 cm , it should be 10 cm.

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.

-------------------------------------------

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.