Prisms are geometric solids that come in many different shapes and an infinite number of sizes. Prism are often distinguished by the shape of their base polygon. A prism having trapezoid base faces is called a trapezoidal prism.

Where, a, b be length of the top and bottom of the trapezoid and h be the height of the trapezoidal. And 'l' be the length or height of the trapezoidal prism.

## Volume of a Trapezoidal Prism

The volume of a right trapezoidal prism is equal to the height times the base area of the trapezoid. The area of trapezoid is $\frac{1}{2}$h(a + b) and 'h' is the height of the trapezoid, not the height of the prism. If 'a' is the length of the top, 'b' is the length of the bottom. Then the formula for the volume of the trapezoidal prism is given below:

### Volume of a Trapezoidal Prism Formula

The volume of a prism is given by the formula,

V = Al

Where A is the area of the base of the prism and 'l' is the length or height of the prism.

=> Area of trapezoidal prism = $\frac{1}{2}$h(a + b)

=> Volume of the Trapezoidal Prism = $\frac{1}{2}$h(a + b) x l

= $\frac{1}{2}$h(a + b)l

Formula:

Volume of the Trapezoidal Prism =
$\frac{1}{2}$h(a + b)l

Where, a = Length of the top, b = Length of the bottom, h = Height of the trapezoidal and l = Height of the prism.

## Surface Area of a Trapezoidal Prism

The surface area of a prism is a sum of its equal bottoms and top faces plus areas of its side's faces. The surface area of a right trapezoidal prism with a bottom equal to a trapezoid with bases 'a' and 'b', other sides 'c','d' and an altitude 'h', which side edge is 'l', be represented by formula a(l + h) + b(l + h) + lc + ld.

### Surface Area of a Trapezoidal Prism Formula

For any prism,
Surface Area of a Prism = L + 2A

Where, L is the lateral surface area and A is the base area of the prism.

Lateral Surface area of the trapezoidal prism (L) = la + lb + lc + ld

and area of bases of the trapezoidal prism (A) = 2 x $\frac{1}{2}$(a + b)h

Because, area of a trapezium = $\frac{1}{2}$(a + b)h

Surface area = Sum of area of all face are of the prism

=> SA = (a + b)h + la + lb + lc + ld

= a(l + h) + b(l + h) + lc + ld.
Formula:

Surface Area of a Trapezoidal Prism = a(l + h) + b(l + h) + lc + ld.

Where,
a, b, c, d are sides of the trapezium.
h = Altitude and l = Height of the prism.