# VOLUME OF  A TRAPEZOIDAL PRISM

## About "Volume of a trapezoidal prism"

Volume of a trapezoidal prism :

Prisms are named for the polygons that form their bases. In this lesson, you will focus on prisms whose bases are either triangles or quadrilaterals other than squares and rectangles

Formula for volume of a trapezoidal prism is

=  Base area x Height

## Volume of a trapezoidal prism - Examples

Example 1 :

Find volume of the prism shown below.

Solution :

Step 1 :

In the given prism, the two side walls are trapezoids. If we consider one of the trapezoid side walls as base, the height of the prism would be 22 cm.

So, the given prism is a trapezoidal prism.

Step 2 :

Volume of the given prism is

=  base area x height

or

V  =  b x h

Step 3 :

Find base area

Area of trapezoid with bases of lengths b₁ and b₂ and height h.

Base area (b)  =  (1/2) x (b + b₂)h

Base area (b)  =  (1/2) x (12 + 8)10

Base area  =  100 sq.cm

Step 4 :

Find volume of the prism.

V  =  b x h

V  =  100 x 22

V  =  2200 cubic cm

The volume of the given prism is 2200 cubic cm.

Example 2 :

Cherise is setting up her tent. Her tent is in the shape of a trapezoidal prism shown below. How many cubic feet of space are in her tent ?

Solution :

Step 1 :

To find the number of cubic feet of space in  the tent, we have to find the volume of Cherise's tent.

Step 2 :

Volume of Cherise's tent (Trapezoidal prism) is

=  base area x height

or

V  =  b x h

Step 3 :

Find base area.

Area of trapezoid with bases of lengths b₁ and b₂ and height h.

Base area (b)  =  (1/2) x (b₁ + b₂)h

Base area (b)  =  (1/2) x (6 + 4)4

Base area  =  20 sq.ft

Step 4 :

Find volume of the prism.

V  =  b x h

V  =  20 x 9

V  =  180 cubic.ft

Hence, the number of cubic feet of space in  Cherise's tent is 180.

After having gone through the stuff given above, we hope that the students would have understood, how to find volume of trapezoidal prism

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