When I see these things, I never know whether we're supposed to
include the bottom or not.
Here's what you have to know in order to solve this:
Area of a triangle = (1/2) (base) (height) .
That's it ! The rest is all just arithmetic.
-- It's a little hard to tell from the drawing, but I think
this thing has six sides.
Each side is a triangle, with base = 15m and height = 12m.
Area of each side = (1/2) (15m) (12m) = (1/2) (180m²) = 90 m²
Area of 6 uvum = (6 x 90 m²) = 540 m² . (That's choice-b.)
That takes care of the sides.
If the bottom is supposed to be included, then we notice that
the bottom is a hexagon. That note of "7.5√3 m" looks like
it's the distance from the center of the hexagon to each side.
If you connect that point to each vertex of the hexagon, then
you have 6 triangles down there. Each one has base = 15m
and height = 7.5√3 m .
Area of each section
= (1/2) (15m) (7.5√3 m)
= (1/2) (112.5 √3 m²)
= 56.25 √3 m² .
Area of all 6 uvum = (6) x (56.25 √3 m²) = 337.5 √3 m²
That's roughly 584.6 m² .
If the bottom is supposed to be included in the whole thing,
then the total surface area is
(540 m²) + (584.6 m²) = 1,124.6 m² (That's choice-c.)
I'm pretty sure the bottom is supposed to be included,
and choice-c is the correct answer.
Otherwise, there would have been no reason to bother
giving us that "7.5√3 m" measurement on the bottom.
