Question

5cm
Area of the shaded.
portion in the given
figure is:
gen
*
tom
​

Answer 1

Answer :

(d). 10 cm²

1st Approach :

Area of shaded region

= Area of ∆LMN + Area of rect. CDLN

= ½•base•height + length•breadth

= ½•5•2 + 5•1

= 5 + 5

= 10 cm²

2nd Approach :

Area of shaded region

= Area of trapezium CDLM

= ½•(sum of parallel sides)•altitude

= ½•(1 + 3)•5

= ½•4•5

= ½•20

= 10 cm²

3rd Approach :

Clearly , LM divides the rectangle ABCD into two congruent trapeziums namely trap. ABML and trap. CDLM .

Thus ,

Ar. of trap. ABML = Ar. of trap. CDLM

Also ,

=> Ar. of rectangle ABCD

= Ar. of trap. ABML + Ar. of trap. CDLM

=> Ar. of rectangle ABCD

= Ar. of trap. CDLM + Ar. of trap. CDLM

=> Ar. of rect.ABCD = 2•(Ar. of trap.CDLM)

=> Ar. of trap.CDLM = ½•(Ar. of rect.ABCD)

=> Area of trap.CDLM = ½•length•breadth

=> Area of trap.CDLM = ½•5•4

=> Area of trap.CDLM = ½•20

=> Area of trap.CDLM = 10

=> Area of shaded region = 10 cm²

Hence ,

Area of shaded region is 10 cm² .