Question

A sheet of paper measures 50cm by 30 cm.A strip 6cm wide is cut from all around. Find the area of the remaining sheet and also the area of the strip cut out.

Answer 1

Hint: Using the formula \[l\times b\]of area for rectangle which is \[l\times b\] here l=50cm and b=30cm is given we will find the total area of rectangle , now 6cm strip is cut from all around so for the remaining paper we will find our new length and new breadth which will be \[50-6=44\]m and \[30-6=24\] , now using formula \[l\times b\] we will find the area of remaining paper also. And the area of paper strip that cut out will be \[area\_old-area\_new\]

Complete step-by-step answer:
We are given a paper which measures 50cm by 30cm, now it is given that a strip of 6cm wide is cut from all 4 corners, we have to find the area of the remaining sheet and also the area of the strip cut out. Using the formula of area of rectangle \[l\times b\], here l is the length and b is the breadth.
First case: we are given length (l=50cm) and breadth (b=30cm) so using formula \[l\times b\]
Area of sheet will be \[area\_old=50\times 30=1500\]
Now 6cm strip is cut from all 4 corners which changes the length and breadth so new length will be equal to \[50-6-6=38\] and new breadth will equal to \[30-6-6=18\]
Second case: now the new length equals to \[50-6-6=38\] and new breadth equal to \[30-6-6=18\] so suing formula \[l\times b\] our new area will be
\[area\_new=38\times 18=684c{{m}^{2}}\]
And the area of the strip cut out will be equals to \[area\_old-area\_new\] putting the values we get \[1500-684=816c{{m}^{2}}\]
Hence the get area of the remaining sheet will be \[area\_new=38\times 18=684c{{m}^{2}}\]and the area of strip cut out will be \[1500-684=816c{{m}^{2}}\]

Note: Most of the students make one common mistake that when calculating new length/breadth they subtract 6 from old length and not 12. We subtract 12 because 6 we subtract from top side and 6, we subtract from bottom side.