- Surface Areas
- Home
- Nets of solids
- Surface area of a cube or a rectangular prism
- Surface area of a rectangular prism made of unit cubes
- Distinguishing between surface area and volume
- Using a net to find the surface area of a rectangular prism
- Word problem involving the surface area of a rectangular prism
- Surface area of a triangular prism
- Using a net to find the surface area of a triangular prism

# Surface area of a cube or a rectangular prism

In this lesson, we will learn how to calculate the surface area of a rectangular prism and solve problems on surface area of rectangular prisms.

A **prism** is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base. The other faces are in the shape of rectangles. They are called lateral faces.

The following diagram shows a rectangular prism.

A **right prism** is a prism that has its bases perpendicular to its lateral surfaces.

The **surface area** of a prism is the total area of all its external faces.

**To calculate the surface area of a rectangular prism**

We calculate the area of each of the six faces of the prism.

We then add up all the areas to get the total surface area.

**Formula to find the surface area of a prism**

Surface area of prism = 2 × area of base + perimeter of base × height of prism

**Formula to find the surface area of a rectangular prism**

Surface area of a rectangular prism = 2 (l × w + w × h + l × h)

Where,

l – length of the prism

w – width of the prism and

h – height of the prism

Find the surface area of the given rectangular prism in square cm.

### Solution

**Step 1:**

Surface area of a rectangular prism = 2(l × w + w × h + 1 × h); l = 3 cm; w = 5 cm; h = 9 cm

**Step 2:**

Surface area of given prism = 2(3 × 5 + 3 × 9 + 9 × 5)

= 2(15 + 27 + 45)

= 174 square cm

Find the surface area of the given rectangular prism in square cm.

### Solution

**Step 1:**

Surface area of a rectangular prism = 2(l × w + w × h + l × h); l = 9 cm; w = 3 cm; h = 2 cm

**Step 2:**

Surface area of given prism = 2(9 × 3 + 9 × 2 + 3 × 2)

= 2(27 + 18 + 6)

= 102 square cm