Question

The central hall of a school is 18m long and 12.5m wide. A carpet is to be laid on the floor leaving a strip 50cm wide near the walls, uncovered. Find the area of the carpet and also the uncovered portion.

Answer 1

Hint:
Here, we have to calculate the area of the carpet by subtracting the size of the strip from the length and breadth of the central hall and then applying the formula of area. Then after finding the area of the carpet to find the uncovered area we have to subtract the area of the carpet from the total area of the central hall.

Complete step by step solution:
It is given that the length of the central hall is 18m and the breadth of the central hall is 12.5m.
Width of the strip to leave on the side of floor is \[{\rm{50cm = 0}}{\rm{.5m}}\]
Now we have to calculate the length and breadth of the carpet to find its area
So the length of the carpet \[{\text{ = length of the floor - 2}} \times {\text{width of the strip}}\]
Length of the carpet \[{\rm{ = 18 - (2}} \times {\rm{0}}{\rm{.5) = 18 - 1 = 17m}}\]
Now, breadth of the carpet \[{\text{ = breadth of the floor - 2}} \times {\text{width of the strip}}\]
Breadth of the carpet \[{\rm{ = 12}}{\rm{.5 - (2}} \times {\rm{0}}{\rm{.5) = 12}}{\rm{.5 - 1 = 11}}{\rm{.5m}}\]
Therefore, area of the carpet \[{\text{ = length of the floor}} \times {\text{breadth of the floor}}\]
Area of the carpet \[{\rm{ = 17}} \times {\rm{11}}{\rm{.5 = 195}}{\rm{.5 }}{{\rm{m}}^2}\]
Now, to find the uncovered area we have to subtract the area of the carpet from the total area of the floor.
Total area of the floor \[{\rm{ = 18}} \times {\rm{12}}{\rm{.5 = 225 }}{{\rm{m}}^2}\]
Therefore, uncovered area \[{\text{ = Total area of the floor - Area of the carpet}}\]
Uncovered area \[{\rm{ = 225 - 195}}{\rm{.5 = 29}}{\rm{.5 }}{{\rm{m}}^2}\]

Hence, \[{\rm{195}}{\rm{.5 }}{{\rm{m}}^2}\] is the area of the carpet and \[{\rm{29}}{\rm{.5 }}{{\rm{m}}^2}\] is the uncovered area.

Note:
Perimeter is the total length of the outer boundary of a shape in two dimensional. Perimeter is measured in meters. Area is the amount of surface covered by a shape in two dimensional. Surface area is the sum of all the areas of the faces of an object or shape. Area and surface area is measured in square meters. Volume is the amount of space occupied by an object in three-dimensional space. Volume is measured in cubic meters.
It is important to write the units of measurement with the values.