9514 1404 393
Answer:
- length: 40 m
- perimeter: 136 m
- area: 653 m²
- volume: 6.52 m³
Step-by-step explanation:
1.
The outer dimensions of the property are 20 squares (length) by 14 squares. Each square is 2 m on a side, so the overall length of the property is ...
(20 squares)×(2 m/square) = 40 m . . . . length
The overall width of the property is ...
(14 squares)×(2 m/square) = 28 m . . . . width
Then the perimeter is ...
P = 2(length + width) = 2(40 +28) m = 136 m . . . . perimeter
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Additional comment
We have computed the perimeter as though the plot were a rectangle. If you carefully consider the total length of horizontal edges and the total length of vertical edges, you see that those totals are the same as they would be for a 20×14 square (40×28 m) rectangle.
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2.
The area of open ground is perhaps most easily computed by finding the area that must be subtracted from the overall 20×14 square rectangle. Those exclusions will be (in dimensions of squares) ...
- lower right corner: 8 wide by 3 high = 24 squares
- fish pond: 2 wide by 3 high = 6 squares
- veranda: 4 wide by 4 high = 16 squares
- house: 9 wide by 7 high = 63 squares
- pavement: 4 wide by 2 high = 8 squares
The total area of exclusions is 24+6+16+63+8 = 117 squares. The bounding rectangle is 20 by 14 = 280 squares, so the open ground is ...
280 squares - 117 squares = 163 squares
At (2 m)(2 m) = 4 m² per grid square, that's an area of ...
(163 squares)(4 m²/square) = 652 m²
The surface area of the open ground is 652 m².
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3.
The volume is given by the formula ...
V = Bh
where B is the base area and h is the height.
1 cm = 1/100 m = 0.01 m thickness. That means the total volume is ...
V = (652 m²)(0.01 m) = 6.52 m³
6.52 cubic meters of topsoil are needed to cover the open ground to a depth of 1 cm.
