Question

A triangular prism has a Surface Area of 134.94 km2. The base of the prism is an equilateral triangle with a height of 3 km and an unknown base. The distance between the bases of the prism is 12 km. Find the measure of the base of the triangle. 4.8 3.9 2.5 3.46

Answer 1

A is surface area of prism. h is height (distance between the bases). b is length of a side of the base triangle. a is the altitude of the base triangle. Then,

A = 2 x base triangle + 3 x area of side panel

A = 2(1/2)ba + 3bh

48.735 = 3b + 3b(12) = 3b(1 + 12) = 39b

b = 48.735 / 39 = 1.250 km. (Answer)

Explanation:

Answer 2

3.46 km is the measure of the base of the triangle.

Explanation:

Base of the prism is an equilateral triangle.

The length of the one of the side or base of the triangle = a

Height of the equilateral triangle,h = 3 km

Area of triangle = A

`A=(1)/(2)* a* h`

Height of the triangular prism = h' = 12 km

Area of rectangle =
`A'=a* h'=a* 12 km`

Area of the triangular prism =
`134.94 km^2`

`134.94 km^2=2* A+3* A'`

(In triangular prism there are two triangles bases and three rectangles)

`134.94 km^2=2* (1)/(2)a* 3 km+3* a* 12`

`134.94 km^2=39a`

a = 3.46 km

3.46 km is the measure of the base of the triangle.