Question

a poster measuring 20 cm and 16 cm is pasted on a sheet of cardboard such that there is a margin of 3.5 cm along each side of the poster .find
a) the total area of the margin
b) the cost of cardboard used at the rate of 1.50 rs per sq.cm.​

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student-nameBristy Baruah asked in Math

Q. A poster of size 20 cm by 16 cm is pasted on a sheet of cardboard such that there is a margin of 3.5 cm along each side of the poster . Find

(i) the total area of a margin

(ii) the cost of the cardboard used at the rate of Rs. 1.20 per cm2

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student-nameSruti Stuti answered this

6 unhelpful votes in Math, Class VII

the total area of margin is 301sq.cm

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student-nameSantanu Sahoo answered this

489 helpful votes in Math, Class X

Dear Bristy,

Here is the answer to your query.

1)

Let ABCD be the given picture.

Then EFGH is the cardboard.

also PA = DQ = DR = CS = 3.5 (margin)

Now EH = PQ = PA + AD + DQ = 3.5 cm + 20 cm + 3.5 cm = 27 cm

and HG = RD + DC + CS = 3.5 cm + 16 cm + 3.5 cm = 23 cm

we know that area of rectangle = Length × breadth

⇒ Area of picture (ABCD) = AD × DC = 20 cm × 16 cm = 320 cm2

and Area of cardboard (EFGH) = EH × HG = 27 cm × 23 cm = 621 cm2 ... (1)

Hence Area of margin = Area of cardboard – Area of picture

= 621 cm2 – 320 cm2 = 301 cm2 ... (ANS)

2)

Area of the cardboard = (320 + 301) cm2

= 621 cm2 -- {Proved above in (1)}

Cost per cm2 = Rs. 1.50

Cost of the cardboard = Rs. (621 x 1.50)

= Rs. 931.5 -- (ANS)