In these lessons, we will learn how to

**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}

*x* is 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?**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

- 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} = 6*x* cm^{2}

Sum of area

30 + 20 + 10 + 6*x* = 72

60 + 6*x* = 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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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