Question

Two identical prisms with base a right angled triangle are joined together to form a rectangular prism, as in the picture below:

What is the surface area of this rectangular prism?

Answer 1

Lengths of sides of the base of the triangular prism are 12 cm and 5 cm.

Height of the triangular prism = 15 cm

Two triangular prisms are joined together to form a rectangular prism.

∴ Length of the base of the rectangular prism = 12 cm

Breadth of the base of the rectangular prism = 5 cm

Height of the rectangular prism = 15 cm

Base perimeter of the rectangular prism = 2 (Length + Breadth)

= 2 (12 + 5) cm

= 2 × 17 cm

= 34 cm

Lateral surface area of the rectangular prism = Height × Base perimeter

= 15 × 34 cm²

= 510 cm²

Base area of the rectangular prism = Length × Breadth

= 5 × 12 cm²

= 60 cm²

Surface area of the rectangular prism = Lateral surface area + 2 × Base area

= (510 + 2 × 60) cm²

= (510 + 120) cm²

= 630 cm²