Lateral Area Trapezoidal Prism Calculator

The lateral area is the sum of the areas of all the sides of an 3D object besides the base and the top. Check out our rectangular prism calculator for more information.

To understand the calculation of the lateral area of a trapezoidal prism, let's take the following trapezoidal prism as an example:

• Side a: 4 m
• Side b: 7 m
• Side c: 4 m
• Side d: 3 m
• Length (ℓ): 10 m
• Height (h): 7 m

You can calculate the lateral area of a trapezoidal prism in four steps:

1. Determine the length (ℓ)

   In this example, the length of the trapezoidal prism is 10 m.

2. Determine the height (h)

   For our example, the height of the trapezoidal prism is 7 m.

3. Determine the lengths of sides a, b, c, and d

   You can see sides a, b, c and d in the diagram. For this trapezoidal prism, these lengths are 4 m, 7 m, 4 m, and 3 m respectively.

4. Compute the volume of the trapezoidal prism

   The last step is to compute the lateral area using the following formula:

   lateral area = ℓ × (a+b+c+d)

   Hence, the lateral area of this trapezoidal prism is 10 m × (4 m + 7 m + 4 m + 3 m) = 180 m².

After understanding how to find the lateral area of a trapezoidal prism, let's talk about surface area. The surface area is the sum of the areas of all the sides of an 3D object, incising its base and top.

For the surface area calculation, we will use the same trapezoidal prism as the last example.

You can calculate the surface area of a trapezoidal prism in four steps:

1. Determine the length (ℓ)

   The same as before, the length of the trapezoidal prism is 10 m.

2. Determine the height (h)

   The height of the trapezoidal prism is 7 m.

3. Determine the lengths of sides a, b, c, and d

   Following the diagram, you can see the side a, side b, side c, and side d of the trapezoidal prism are 4 m, 7 m, 4 m, and 3 m respectively.

4. Calculate the surface area of the trapezoidal prism

   The last step is to compute the surface area using the following formula:

   surface area = h×(b+d) + ℓ×(a+b+c+d)

   Hence, the surface area of this trapezoidal prism is 7 m × (7 m + 3 m) + 10 m × (4 m + 7 m + 4 m + 3 m) = 250 m².