40 square yards of the plastic used.
What is rectangular prism?
"It is a three-dimensional solid shape which has six faces that are rectangles."
What is the surface area of the rectangular prism?
A = 2 × ( w × l + h × l + h × w)
where, 'w' is the width of the rectangular prism
'l' is the length of the rectangular prism
'h' is the height of the rectangular prism
For given example,
A pond is created by digging a rectangular prism. The hole is 3 yards wide, 4 yards long, and 2 yards deep.
the width of the pond (w) = 3 yards
the length of the pond (l) = 4 yards
the height (for this example depth) of the pond (h) = 2 yards
The sides and bottom of the pond are lined with a protective plastic.
We need to find the amount of plastic used.
Since the top of the pond in open,
The area occupied by the plastic = area of the rectangular prism - area of the top surface of the rectangular prism
By using the formula of the surface area of the rectangular prism,
⇒ A1 = 2 × ( w × l + h × l + h × w)
⇒ A1 = 2 × ( 3 × 4 + 2 × 4 + 2 × 3)
⇒ A1 = 2 × (12 + 8 + 6)
⇒ A1 = 2 × 26
⇒ A1 = 52 square yards
Area of the top surface of the pond would be,
[tex]\Rightarrow A_T = l\times w\\\\\Rightarrow A_T = 4\times 3\\\\\Rightarrow A_T = 12~square~yards[/tex]
So, the required area is,
[tex]\Rightarrow A = A1-A_T\\\\\Rightarrow A=52-12\\\\\Rightarrow A=40~square~yards[/tex]
Therefore, 40 square yards of the plastic used.
Learn more about the rectangular prism here:
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