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

Answer:

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

Step-by-step 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

$A=\frac{1}{2}\times a\times h$

Height of the triangular prism = h' = 12 km

Area of rectangle =$A'=a\times h'=a\times 12 km$

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

$134.94 km^2=2\times A+3\times A'$

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

$134.94 km^2=2\times \frac{1}{2}a\times 3 km+3\times a\times 12$

$134.94 km^2=39a$

a = 3.46 km

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

Answer 2

Answer:

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)

Step-by-step explanation: