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..
Trapezoidal Prism
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.
Trapezoidal Prism Net
Formulas
Surface Area
The formula is given below:
Total Surface Area (TSA) = (a + b) × h+ (a + b + c + d)× l, here a = long base edge, b = short base edge, c and d = slant base edges, h = height, l = length
Also, since Lateral Surface Area (LSA) = Base perimeter x height
Here, Base Perimeter = (a + b + c + d) × l
∴ Lateral Surface Area (LSA) = (a + b + c + d) × l
Thus, we can write
Total Surface Area (TSA) = (a + b) × h+ LSA
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 m2 Total Surface Area (TSA) = (a + b) × h+ LSA, here a = 14 m, b = 11 m, LSA = 273 m2 ∴TSA = (14 + 11) × 5 + 273 = 398 m2
Volume
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 ft3 Converting ft to liters, Given, 1 cubic ft = 28.32 liters ∴27.5 ft3 = 27.5 × 28.32 liters = 778.8 liters
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)