find the area of borbder.
if inner lenght = 100m inner breadth = 50m , width of the border = 2m
Solution
To find the area of the border, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
Step 1: Calculate the area of the inner rectangle.
Given: Inner length = 100m, Inner breadth = 50m.
Area of inner rectangle = Inner length × Inner breadth
= 100m × 50m
= 5000 square meters.
Step 2: Calculate the area of the outer rectangle.
Given: Width of the border = 2m.
To find the length and breadth of the outer rectangle, we need to add twice the width of the border to the length and breadth of the inner rectangle.
Length of outer rectangle = Inner length + 2 × Width of the border
= 100m + 2 × 2m
= 100m + 4m
= 104m.
Breadth of outer rectangle = Inner breadth + 2 × Width of the border
= 50m + 2 × 2m
= 50m + 4m
= 54m.
Area of outer rectangle = Length of outer rectangle × Breadth of outer rectangle
= 104m × 54m
= 5616 square meters.
Step 3: Calculate the area of the border.
Area of border = Area of outer rectangle - Area of inner rectangle
= 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 border, we first need to find the dimensions of the outer rectangle.
Since the inner length is given as 100m and the border has a width of 2m, the outer length would be equal to the inner length plus twice the width of the border.
Outer length = Inner length + (2 x Width of border)
Outer length = 100m + (2 x 2m)
Outer length = 100m + 4m
Outer length = 104m
Similarly, since the inner breadth is given as 50m and the border has a width of 2m, the outer breadth would be equal to the inner breadth plus twice the width of the border.
Outer breadth = Inner breadth + (2 x Width of border)
Outer breadth = 50m + (2 x 2m)
Outer breadth = 50m + 4m
Outer breadth = 54m
Now that we have the dimensions of the outer rectangle (104m x 54m) and the inner rectangle (100m x 50m), we can find the area of the border.
Area of the border = (Outer length x Outer breadth) - (Inner length x Inner breadth)
Area of the border = (104m x 54m) - (100m x 50m)
Area of the border = 5616m² - 5000m²
Area of the border = 616m²
Therefore, the area of the border is 616 square meters.
inner area: 100*50
outer area: (100+2*2)(50+2*2)
border area = (outer area) - (inner area)