Question

The perimeter of a triangular prism is 36 cm and lateral surface area is 720 sq cms. if the base is an equilateral triangle then
a) what is the height of the prism?
b) find the total ssurface area of prism.

Answer 1

Prism height = 20 cm , Total Surface area of prism =  844.7 cm²

Step-by-step explanation:

The Base perimeter of a triangular prism =  36 cm

Side of Triangle = 36/3 = 12 cm

Height of Prism =  h cm

Lateral Surface Area = (Base perimeter) * height

=> 720 =  36 * h

=> h = 20

Prism height = 20 cm

Total Surface area of prism = 2 * Base Area  + Lateral Surface area

= 2 * (√3 / 4) * 12²  + 720

= 124.7 + 720

= 844.7 cm²

Total Surface area of prism =  844.7 cm²

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Answer 2

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The Base perimeter of a triangular prism = 36 cm

Side of Triangle = 36/3 = 12 cm

Height of Prism = h cm

Lateral Surface Area = (Base perimeter) * height

=> 720 = 36 * h

=> h = 20

Prism height = 20 cm

Total Surface area of prism = 2 * Base Area + Lateral Surface area

= 2 * (√3 / 4) * 12² + 720

= 124.7 + 720

= 844.7 cm²

Total Surface area of prism = 844.7 cm²