The base of a prism is an equilateral triangle of perimeter 12 centimetres and its height is 5 centimetres. What is its total surface area?

Given: base of a prism is an equilateral triangle and its perimeter “p” = 12cm

Height of the prism “h” = 5cm

To find : total surface area of the prism = ?

Procedure :

Now, we know that,

total surface area of the prism = lateral surface area of the prism + 2× (area of base of the prism)

⇒ first we will find the side of the triangular base of the prism.

So, perimeter of the equilateral triangle = 3×side

⇒ 12 = 3×side

⇒ Side = 4cm

now, to find the lateral surface area, we have

⇒ Lateral surface area =perimeter of base of prism × height of prism

= 12 × 5

= 60cm²

Now, we can find the total surface area of the prism.

So, total surface area of the prism = lateral surface area of the prism + 2× (area of base of the prism)

⇒ total surface area of the prism = 60 + 2×(area of equilateral triangle)

⇒ total surface area of the prism = 60 + 2×(× side²)

= 60 + 2× (×4²)

= 60 + 8√3

= 60 + 13.856

= 73.856cm²

∴ Total surface area of the given prism is 73.856cm²