Answer:
C
Step-by-step explanation:
the total surface area of such a pyramid is the sum of 5 areas :
1 bottom square (8×8)
4 side triangles
the area of a triangle is
baseline × height / 2
now, we know the baseline of the 4 triangles, but what is their height (at least we know, all 4 have the same height, as the pyramid is totally regular) ?
the height of the side triangles is the slant height of the pyramid (the distance from the middle of a sideline to the top of the pyramid).
we get this by imagining a right-angled triangle inside the pyramid :
one leg is the inner height of the pyramid.
the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.
and the baseline (Hypotenuse) is the slant height of the pyramid.
we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle).
slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65
slant height = sqrt(65) = 8.062257748... in
so, we get a areas
bottom square = 8×8 = 64 in²
a side triangle = 8×sqrt(65)/2 = 4×sqrt(65) =
= 32.24903099... in²
all 4 side triangles = 4×32.24903099... =
= 128.996124... in²
and we get as total surface area
64 + 128.996124... = 192.996124... in² ≈ 193.00 in²
by
. Then the line integral is
, then
