How To Find Volume Of Trapezium Prism

Volume OF  A TRAPEZOIDAL PRISM

Prisms are named for the polygons that form their bases. In this lesson, yous 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 Elevation

Example 1 :

Find volume of the prism shown below.

Solution :

Step 1 :

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

And so, the given prism is a trapezoidal prism.

Footstep 2 :

Volume of the given prism is

  =  base area 10 height

or

V  =  b x h

Pace three :

Find base area

Area of trapezoid with bases of lengths b ₁  and b ₂  and height h.

Base area (b)  =  (1/2) x ( b₁  + b₂ )h

Base area (b)  =  (one/ii) ten (12  + 8 )10

Base area  =  100 sq.cm

Step 4 :

Find volume of the prism.

V  =  b 10 h

V  =  100 x 22

V  =  2200 cubic cm

The volume of the given prism is 2200 cubic cm.

Instance 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 observe the book of Cherise's  tent.

Step 2 :

Volume of Cherise'south  tent (Trapezoidal prism) is

  =  base of operations area 10 elevation

or

V  =  b x h

Step 3 :

Find base area.

Area of trapezoid with bases of lengths b ₁  and b ₂  and height h.

Base area (b)  =  (1/ii) x(b₁  + b₂ ) h

Base area (b)  =  (1/2) 10 (6  + 4 )4

Base area  =  20 sq.ft

Pace 4 :

Find volume of the prism.

Five  =  b ten h

V  =  20 x 9

V  =  180 cubic.ft

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

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