Question

What is the surface area of a rectangular prism with a height of 6 yd length of 5.4 yd and width of 3.8 yd

Answer 1

Sure, here's how to calculate the surface area of a rectangular prism with the given dimensions:

First, we can calculate the area of each face of the rectangular prism. The top and bottom faces each have an area of length times width, or lw:

`\sf A_(top/bottom) = lw = 5.4\text{ yd} * 3.8\text{ yd} = 20.52\text{ yd}^2`

The front and back faces each have an area of height times width, or hw:

`\sf A_(front/back) = hw = 6\text{ yd} * 3.8\text{ yd} = 22.8\text{ yd}^2`

The left and right faces each have an area of length times height, or lh:

`\sf A_(left/right) = lh = 5.4\text{ yd} * 6\text{ yd} = 32.4\text{ yd}^2`

To find the total surface area of the rectangular prism, we add up the areas of all six faces:

`\sf A_(total) = 2A_(top/bottom) + 2A_(front/back) + 2A_(left/right)`

Substituting in the values we calculated earlier, we get:

`\sf A_(total) = 2(20.52\text{ yd}^2) + 2(22.8\text{ yd}^2) + 2(32.4\text{ yd}^2) = 198.72\text{ yd}^2`

Therefore, the surface area of the rectangular prism is 198.72 square yards.

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Answer 2

• The surface area is 151.44 yd²

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Total surface area of a rectangular prism with dimensions of l, w and h is:

• A = 2(lw + lh + wh), as it has six faces with same opposite faces

Given dimensions:

• l = 5.4 yd, w = 3.8 yd and h = 6 yd

Substitute the values into the formula and calculate the toal surface area:

• A = 2(5.4*3.8 + 5.4*6 + 3.8*6) = 151.44 yd²