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PIT_PIT [208]
3 years ago
14

How to do number 5 ? And are the rest right ?

Mathematics
1 answer:
Fantom [35]3 years ago
8 0
I think you did all your other questions right and here i attached the photo for how to do number 5

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They should be 54 students who know how to salsa

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Surface Area of the pyramid
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C

Step-by-step explanation:

the total surface area of such a pyramid is the sum of 5 areas :

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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

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237 is the answer i think
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