Question

find the total surface area of the prism.
\\(sa = ?\text{ cm}^2\\)

Explanation:

Identify the dimensions of the rectangular prism

The given solid is a rectangular prism. From the image, we can identify its three dimensions:

• Length \(l = 25\text{ cm}\)
• Width \(w = 9\text{ cm}\)
• Height \(h = 10\text{ cm}\)

State the surface area formula

The total surface area (\(SA\)) of a rectangular prism is calculated by finding the sum of the areas of all six faces:

$$SA = 2(lw + lh + wh)$$

Calculate the area of each pair of opposite faces

We compute the products of the dimensions:

• Front and back faces: \(l \times h = 25 \times 10 = 250\text{ cm}^2\)
• Top and bottom faces: \(l \times w = 25 \times 9 = 225\text{ cm}^2\)
• Left and right faces: \(w \times h = 9 \times 10 = 90\text{ cm}^2\)

Sum the areas and multiply by two

We add these areas together and multiply by \(2\) to find the total surface area:

$$SA = 2(225 + 250 + 90)$$

$$SA = 2(565)$$

$$SA = 1130\text{ cm}^2$$

Answer:

Find the total surface area of the prism.

\(SA =\) <blank>1130</blank> \(\text{cm}^2\)