What is the formula for calculating the surface area of a rectangular prism?

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UpStudy AI · Accepted Answer

The surface area of a rectangular prism (also known as a cuboid) can be calculated using the formula:

$$
\text{Surface Area} = 2lw + 2lh + 2wh
$$

**Where:**
- $$ l $$ = length
- $$ w $$ = width
- $$ h $$ = height

**Simplified Formula:**
$$
\text{Surface Area} = 2(lw + lh + wh)
$$

**Explanation:**
A rectangular prism has six faces:
- **Top and Bottom:** Each with an area of $$ lw $$
- **Front and Back:** Each with an area of $$ lh $$
- **Left and Right Sides:** Each with an area of $$ wh $$

By calculating the area of each pair of identical faces and summing them up, you obtain the total surface area.

**Example:**
Suppose you have a rectangular prism with:
- Length ($$ l $$) = 5 units
- Width ($$ w $$) = 3 units
- Height ($$ h $$) = 2 units

Plugging these values into the formula:

$$
\text{Surface Area} = 2(5 \times 3) + 2(5 \times 2) + 2(3 \times 2) = 2(15) + 2(10) + 2(6) = 30 + 20 + 12 = 62 \text{ square units}
$$

So, the surface area of the rectangular prism is **62 square units**.

**Summary:**
To find the surface area of a rectangular prism, multiply each pair of dimensions, sum those products, and then multiply by two:

$$
\text{Surface Area} = 2(lw + lh + wh)
$$
The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula is: $$ \text{Surface Area} = 2(lw + lh + wh) $$ Where: - $$ l $$ = length - $$ w $$ = width - $$ h $$ = height

What is the formula for calculating the surface area of a rectangular prism?

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