a right equilateral triangular prism with base edge length 8ft and height 14 ft, help please  dont know how to get the answer

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The problem does not ask for volume or total surface area, hence, until the request of the problem will be provided, you may evaluate the followings:

TSA (total surface area) = 3*Area of side + 2*Area of base

The sides of prism are rectangles, hence you need to use the following formula to evaluate the area:

A = length*width `= 14*8 = 112 ft^2`

The base of prism is equilateral triangle, hence you need to use the following formula to evaluate the area:

`A = (l^2*sin 60^o)/2 =gt A = 64*sqrt3/4`

`A = 16*sqrt3 ft^2`

`TSA = (112 + 16*sqrt3) ft^2`

You need to evaluate the volume of right triangular prism such that:

V = A of  base*height

`V = 16*sqrt3*14 =gt V = 224sqrt3 ft^3`

Hence, evaluating the TSA and Volume of prism yields `TSA = (112 + 16*sqrt3) ft^2`  and `V = 224sqrt3 ft^3` .

najm1947's profile pic

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

The area of the equilateral triangle = sqrt(3)*a^2/4 where a is the side

The area of base = sqrt(3)*8^2/4 = 27.71 sq.ft.

If you are interested in the surface area of the prism of height 14 ft then:

Surface area prism = 2*27.71+3*8*14 = 391.42 sq.ft

If you are interested in volume of the prism then:

Volume of prism = 27.71*14 = 387.94 ft3

The surface area of prism is 391.42 ft2

The volume of prism is 387.94 ft3

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