Related Topics: More Geometry Lessons

In these lessons, we will learn how to

• calculate the surface area of prisms: rectangular prisms, triangular prisms, trapezoidal prisms, hexagonal prisms etc.

• solve problems about prisms.

• calculate the surface area of prisms using nets.

**What is a Prism?**

**How to calculate the surface area of a prism?**

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

= 2 × 6 + (3 + 4 + 5) × 7 = 96 cm^{2}

### How to find the Surface Area of different types of Prisms

This video shows how to find the surface area of prisms: cuboid
(or rectangular prism), triangular prism, trapezoidal prism.
**How to find the surface area of a
rectangular prism?**
**How to find the surface area of a triangular
prism using the formula SA = ab+(s1+s2+s3)h?**
**How to find the surface area of a pentagonal
prism?**
**How to find the surface area of a hexagonal
prism?**
**How to find the surface area of a octagonal
prism?**

### Word problems about prisms

How to find the surface area of prisms and cylinders using a given formula? How to solve word problems and composite figures?

Problem: A treasure chest is a composite figure. If you were to paint the surface area, how many square feet would you paint? Round your answer to the nearest feet.### Surface area of prisms using nets

This video shows how to find the surface area of a cube, rectangular prism and triangular prism using nets.
**How to find the surface area of a hexagonal prism using a net?**

In these lessons, we will learn how to

• calculate the surface area of prisms: rectangular prisms, triangular prisms, trapezoidal prisms, hexagonal prisms etc.

• solve problems about prisms.

• calculate the surface area of prisms using nets.

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 parallelograms. They are called lateral faces.

The following diagrams show a triangular prism and a rectangular prism.

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

When we cut a prism parallel to the base, we get a cross section of a prism. The cross section is congruent (same size and shape) as the base, as can be seen in the following diagram.

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

**Step 1: **
Determine the shape of each face.

**Step 2: **Calculate
the area of each face.

**Step 3: **Add up all
the areas to get the total surface area.

We can also use the formula

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

Worksheet to calculate the surface area and volume of a rectangular prism

**Example: **

Calculate the surface area of the following prism.

**Solution: **

There are 2 triangles with the base = 4 cm and height = 3 cm.

Area of the 2 bases

= 12 cm^{2}

1 rectangle with length = 7 cm and width = 5 cm

Area = lw = 7 × 5 = 35 cm^{2}

1 rectangle with length = 7 cm and width 3 m

Area = lw = 7 × 3 = 21 cm^{2}

1 rectangle with length = 7 cm and width 4 m

Area = lw = 7 × 4 = 28 cm^{2}

The total surface area is 12 + 35 + 21 + 28 = 96 cm^{2}

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

= 2 × 6 + (3 + 4 + 5) × 7 = 96 cm

**Example: **

The diagram shows a prism whose base is a trapezoid. The surface
area of the trapezoidal prism is 72 cm^{2}. Find the value of x.

**Solution: **

There are 2 rectangles with length = 5 cm and width = 3 cm

Area = 2 × 5 × 3 = 30 cm^{2}

There is one rectangle with length = 5 cm and width = 4 cm

Area = 5 × 4 = 20 cm^{2}

There is one rectangle with length = 5 cm and width = 2 cm

Area = 5 × 2 = 10 cm^{2}

There are two trapezoids.

Area = cm^{2} = 6x cm^{2}

Sum of area

30 + 20 + 10 + 6x = 72

60 + 6x = 72

x = 2

Problem: A treasure chest is a composite figure. If you were to paint the surface area, how many square feet would you paint? Round your answer to the nearest feet.

Try the free Mathway calculator and
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