Mathematics
A rectangular plot of land measures 45 m x 30 m. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.
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Answer
Given:
The boundary wall is built all around the rectangular plot at a distance of 1 meter, which means the wall forms a larger rectangle around the plot as shown in the figure below:
Dimensions of the outer rectangle (including the boundary wall):
Length of the outer rectangle = (45 + 1 + 1) m = 47 m
Width of the outer rectangle = (30 + 1 + 1) m = 32 m
Perimeter of the outer rectangle = 2(length + breadth)
= 2(47 + 32)
= 2 x 79 = 158 m
Area of the inner surface of the boundary wall is the perimeter of the outer rectangle multiplied by the height of the wall.
Inner surface area of boundary wall = Perimeter of outer rectangle x height of wall
= 158 m x 2.4 m
= 379.2 m2
Hence, the area of the inner surface of the boundary wall is 379.2 m2.
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