a picture is painted on a card  board 8cm long and 5 cm wide such that there is a margin of 1.5cm lomg each of its sides .find the area of the path 

Dear Student!

Here is the answer to your query.

Let ABCD be the given picture.

Then EFGH is the cardboard.

also PA = DQ = DR = CS = 1.5 cm  (margin)

Now EH = PQ = PA + AD + DQ = 1.5 cm + 8 cm + 1.5 cm = 11 cm

and HG = RD + DC + CS = 1.5 cm + 5 cm + 1.5 cm = 8 cm

we know that area of rectangle = Length × breadth

⇒ Area of picture (ABCD) = AD × DC = 8 cm × 5 cm = 40 cm²

and Area of cardboard (EFGH) = EH × HG = 11 cm × 8 cm = 88 cm²

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

= 88 cm² – 40 cm² = 48 cm²

Cheers!