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# How to find the surface area of a trapezoidal prism?

A trapezoidal prism is a three-dimensional solid made up of two trapezoids on opposite faces joined by four rectangles called the lateral faces.

## Answer: The surface area of a trapezoidal prism is h (b + d) + l (a + b + c + d)

We will find the surface area of a trapezoidal prism in few steps.

**Explanation:**

Let's solve this question with the help of a given diagram of the trapezoidal prism.

We know that the base of a prism is in the shape of a trapezoid.

The surface area of the trapezoidal prism (S) = 2 × area of base + lateral surface area ---- (1)

Area of trapezoid = h (b + d)/2 ---- (2)

The lateral surface area of the trapezoidal prism = the sum of the areas of each rectangular surface around the base.

= (a × l) + (b × l) + (c × l) + (d × l) ---- (3)

Put the values from equation (2) and equation (3) in equation (1):

The surface area of the trapezoidal prism (S) = 2 × h (b + d)/2 + (a × l)+(b × l) + (c × l) + (d × l)

S = h (b + d) + a × l + b × l + c × l + d × l

S = h (b + d) + l (a + b + c + d)

### Hence, the surface area of a trapezoidal prism is h(b+d)+l(a+b+c+d).

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