question_answer 1)

A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is \[\alpha \] margin of 1.5 cm along each of its sides. Find the total area of the margin.

Answer:

                Area of the rectangle \[\text{ABCD = l  }\!\!\times\!\!\text{  b}\]                 \[\text{= 8 cm  }\!\!\times\!\!\text{  5 cm = 40 c}{{\text{m}}^{\text{2}}}\] Area of the rectangle PQRS \[=l\times b\] \[=\{8-(1.5+1.5)\}\text{ }cm\text{ }\times \text{ }\{5-(1.5+1.5)\}cm\] \[\text{= 5 cm  }\!\!\times\!\!\text{  2 cm = 10 c}{{\text{m}}^{\text{2}}}\] \[\therefore \]  Total area of the margin                 = Area of the rectangle ABCD ? Area of the rectangle PQRS \[\text{= 40 c}{{\text{m}}^{\text{2}}}\text{-10 c}{{\text{m}}^{\text{2}}}\text{= 30 c}{{\text{m}}^{\text{2}}}\]