The lateral area of the right regular triangular prism is 18 square cm. Find the total surface area. Give answer in decimal form rounded of to 2 decimal places.

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Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the total surface area of the right regular triangular prism, hence, you need to know the lateral area and the area of the bases.

`TSA = L + 2B`

`L` represents the lateral area of the prism

`B` represents the area of the base

The problem provides the value of the lateral area, `18 cm^2` , hence, you may evaluate the area of the base, such that:

`L = 3*3*x = 9x => 18 = 9x => x = 18/9 = 2 cm`

You need to evaluate the area of the base that is the area of equilateral triangle, such that:

`B = 2*2*sqrt3/4 => B = sqrt 3 cm^2`

`TSA = 18 cm^2 + 2sqrt 3 cm^2 => TSA ~~ 21.46 cm^2`

Hence, evaluating the total surface area of the right regular triangular prism, under the given conditions, yields `TSA ~~ 21.46 cm^2.`