Find area of following border
Inner length=100m,Inner breadth =50m,width of border=2m
(100+4)(50+4) - 100*50 = ____
To find the area of the border, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
1. Calculate the area of the inner rectangle:
Area of the inner rectangle = Length × Breadth
Area = 100m × 50m = 5000 square meters
2. Calculate the area of the outer rectangle:
Since the width of the border is 2m, we need to add 2m to the length and breadth of the inner rectangle to get the dimensions of the outer rectangle.
Outer length = Inner length + 2 × Border width = 100m + 2 × 2m = 100m + 4m = 104m
Outer breadth = Inner breadth + 2 × Border width = 50m + 2 × 2m = 50m + 4m = 54m
Area of the outer rectangle = Outer length × Outer breadth
Area = 104m × 54m = 5616 square meters
3. Calculate the area of the border:
Border Area = Area of the outer rectangle - Area of the inner rectangle
Border Area = 5616 square meters - 5000 square meters = 616 square meters
Therefore, the area of the border is 616 square meters.
To find the area of the given border, we first calculate the area of the inner rectangle and then subtract it from the area of the outer rectangle to get the area of the border.
Step 1: Calculate the area of the inner rectangle.
Given:
Inner length = 100m
Inner breadth = 50m
The area of the inner rectangle can be calculated using the formula:
Area = Length x Breadth
Substituting the given values:
Area of inner rectangle = 100m x 50m = 5000 sq. m
Step 2: Calculate the area of the outer rectangle.
Given:
Width of the border = 2m
To calculate the dimensions of the outer rectangle, we add twice the width of the border to the inner dimensions.
Outer length = Inner length + 2 x Width of border
Outer breadth = Inner breadth + 2 x Width of border
Substituting the given values:
Outer length = 100m + 2 x 2m = 100m + 4m = 104m
Outer breadth = 50m + 2 x 2m = 50m + 4m = 54m
The area of the outer rectangle can be calculated using the formula:
Area = Length x Breadth
Substituting the calculated values:
Area of outer rectangle = 104m x 54m = 5616 sq. m
Step 3: Calculate the area of the border.
Area of border = Area of outer rectangle - Area of inner rectangle
Area of border = 5616 sq. m - 5000 sq. m
Area of border = 616 sq. m
Therefore, the area of the given border is 616 square meters.