Nataha Prism Problem

Area of bottom  = (17)*(8)

Area of "top"  = (17)*(10)

Area of "back" = (17)*(6)

Area of sides = 2*(1/2)*(8)*(6) = 48

So we have 

17(8 + 10 + 6) + 48 =

17(24) + 48 =

456 sq m

whoohoo a bunch of rectangles and triangles!

Since the end triangles have side lengths of 6, 8, and 10 they are a pythagorean triple which implies that they are right triangles.  As such each has an area of 6(8)/2=24 m^2

The base is a rectangle with lengths 8 and 17 so its area is 8(17)=136 m^2

The "back" side has lengths of 6 and 17 so its area is 6(17)=102 m^2

And the "top" face has lengths of 10 and 17 so its area is 10(17)=170 m^2

Add them all together and we get 2(24)+136+102+170=456 m^2