Question

the bases of a prism are right triangles with side lengths 6 meters,8 meters,and 10 meters. The height of a prism is 3 meters. What is the lateral area the prism.What is the total surface area?

Answer 1

The way I picture this thing, it's made of three rectangles
that are joined together. 

-- One rectangle is 3 x 6 meters.
-- One rectangle is 3 x 8 meters.
-- One rectangle is 3 x 10 meters.

-- Their 3-meter edges are all taped together to make a 'tube'.

-- It's 3 meters long, and it has 3 sides. 

-- When you look at the ends of the tube, they're both
right triangles with sides of 6, 8, and 10 meters.

-- The area of each side = 1/2 (base x height)

                                         = 1/2(6m x 8m)  =  24 square meters.

                                                       2 ends  =  48 square meters.

-- The lateral surface area is the area of the three rectangles
that make the 'tube'.  

-- Area of the 6 x 3 rectangle = 18 square meters
-- Area of the 8 x 3 rectangle = 24 square meters
-- Area of the 10 x 3 rectangle = 30 square meters

-- Total lateral area = (18 + 24 + 30) = 72 square meters.

-- When you add the ends to it, you get

                 (72 + 48) = 120 square  meters
                                     for the total area.