Two identical prisms with right triangles as base are joined to form a rectangular prism as shown below:

What is its total surface area?

Given: dimensions of triangular prism:

Height = 15cm

Smaller side of right triangular base = 5cm

bigger side of right triangular base = 12cm

To find: total surface area of the newly formed rectangular prism

Procedure:

After joining the 2 identical triangular prisms, we get a new rectangular prism.

⇒ The dimensions of the rectangular prism is:

Length of base = 12cm

Breadth of the base = 5cm

Height of the prism = 15cm

Now total surface area of the rectangular prism = lateral surface area + area of both the bases

We will have to find the lateral surface area of the rectangular prism.

⇒ Lateral surface area = base perimeter × height of prism

= (12+5) × 15

= 255cm²

∴ total surface area of the rectangular prism = 255 + 2× (12× 5)

= 255 + 120

= 375cm²

∴ Total surface area of the newly formed rectangular prism is 375cm²