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:
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
[tex]A=\frac{1}{2}\times a\times h[/tex]
Height of the triangular prism = h' = 12 km
Area of rectangle =[tex]A'=a\times h'=a\times 12 km[/tex]
Area of the triangular prism = [tex]134.94 km^2[/tex]
[tex]134.94 km^2=2\times A+3\times A'[/tex]
(In triangular prism there are two triangles bases and three rectangles)
[tex]134.94 km^2=2\times \frac{1}{2}a\times 3 km+3\times a\times 12[/tex]
[tex]134.94 km^2=39a [/tex]
a = 3.46 km
3.46 km is the measure of the base of the triangle.
