Table of Contents

Last modified on March 28th, 2023

A trapezoidal prism is a three-dimensional solid consisting of two identical trapezoidal faces joined together by four rectangular faces. It has 6 faces (2 trapezoidal and 4 rectangular), 12 edges, and 8 vertices..

Some real-life examples of trapezoidal prisms are bathtubs shaped like hollow trapezoidal prisms and blocks or bricks in round structures like fire pits or wells.

A 2-dimensional net can be used to construct a trapezoidal prism to understand its shape. Generally a net is made from paper and cut in a manner such that it can be folded and modified into 3-D shape as shown below.

The formula is given below:

**Total Surface Area ( TSA) = **

Also**, **since **Lateral Surface Area (*** LSA)* = Base perimeter x height

Here, Base Perimeter = *(a + b + c + d) × l*

∴ **Lateral Surface Area ( LSA) = **

Thus, we can write

**Total Surface Area (****TSA****) = (a + b) × h**

Let us solve an example to understand the concept better.

**Find the lateral and total surface area of a trapezoidal prism whose base edges are 14 m and 11 m, and slant base edges are 6 m and 8 m. The height is 5 m, and its length is 7 m.**

Solution:

As we know,

∴ Lateral Surface Area (*LSA) = (a + b + c + d) × l, *here *a* = 14 m, *b* = 11 m, *c* = 6 m, *d* = 8 m, *h* = 5 m, *l* = 7 m

∴*LSA* = (14 + 11 + 6 + 8) × 7

= 273 m^{2}

Total Surface Area (*TSA*) = *(a + b) × h* *+ LSA, *here *a* = 14 m, *b* = 11 m, *LSA* = 273 m^{2}

∴*TSA* = (14 + 11) × 5 + 273

= 398 m^{2}

The formula is given below:

${Volume\left( V\right) =\dfrac{1}{2}\left( a+b\right) \times h\times l}$, here *a* = long base edge, *b* = short base edge, *h* = height of trapezoidal base, *l* = length

Let us solve an example to understand the concept better.

**Find the volume of a trapezoidal prism-shaped bathtub in the figure, and also the volume of water it can hold. (given 1 cubic ft = 28.32 liters)**

Solution:

Volume of the trapezoidal prism = Volume of water it can hold

As we know,

${Volume\left( V\right) =\dfrac{1}{2}\left( a+b\right) \times h\times l}$*,* here *a* = 6 ft, *b* = 5 ft, *h* = 2 ft, *l* = 2.5 ft,

${\therefore V=\dfrac{1}{2}\times \left( 6+5\right) \times 2×2.5}$

= 27.5 ft^{3}

Converting ft to liters,

Given, 1 cubic ft = 28.32 liters

∴27.5 ft^{3} = 27.5 × 28.32 liters

= 778.8 liters

**More Resources:**- Volume of a Prism
- Surface Area of a Prism
- Right Prism
- Oblique Prism
- Rectangular Prism
- Volume of a Rectangular Prism
- Surface Area of a Rectangular Prism
- Triangular Prism
- Volume of a Triangular Prism
- Surface Area of a Triangular Prism
- Hexagonal Prism
- Volume of a Hexagonal Prism
- Surface Area of a Hexagonal Prism
- Pentagonal Prism
- Volume of a Pentagonal Prism
- Surface Area of a Pentagonal Prism
- Trapezoidal Prism
- Volume of a Trapezoidal Prism
- Surface Area of a Trapezoidal Prism
- Square Prism
- Volume of a Square Prism
- Surface Area of a Square Prism
- Octagonal Prism
- Heptagonal Prism
- Decagonal Prism

Last modified on March 28th, 2023