Question

The surface area of a triangular pyramid is 2304 cm2.

If all the faces of the pyramid are congruent, what is the area of one face of this pyramid?

A.
576 cm2

B.
768 cm2

C.
6912 cm2

D.
9216 cm2

Answer 1

which one do you think it is

Answer 2

i am not sure but i think it might be B

Answer 3

okay

Answer 4

is it B?

Answer 5

@bohotness is it B?

Answer 6

i think your right

Answer 7

:/

Answer 8

ok

Answer 9

@SolomonZelman plz help!

Answer 10

Well, if I'm interpreting your question correctly, ie., "...has an area of 2304 cm^2..." means its base has an area of 2304... we can be comfortable that the pyramid has a base of 48cm x 48cm because 48 x 48 = 2304.

Now, does the "surface area" just include the sides? ( I'm going to assume so - and I think this was a poorly worded question.)

Each side has 1/4 of the surface area... 1536 cm^2.
Each side is a triangle - with a base of 48 cm - and an area of 1536 cm^2

Area of a triangle = 1/2 B*H = 1536 cm^2 = 1/2 48H
The "Height" of the triangular sides is 64 cm.

I put "height" in quotation marks because it is NOT the height of the pyramid. It is the distance measured from the ground up along the slanted surface of the pyramid to its peak.
For the height of the pyramid we use the Pythagorean Theorem, a^2 + b^2 = c^2.

The sloping side, 64cm is the hypotenuse... the "c^2".
"a^2" is 24 cm - 'cause each side only leans in to the middle of the 48 cm wide base.
We are looking for "b^2".

64^2 = 24^2 + b^2
4096 = 576 + b^2
b^2 = 3520
b = 59.33 cm

The pyramid has a 48 x 48 base, is 59.33 cm tall, and you'd have to climb 64 cm to reach its peak.

Answer 11

?????

Answer 12

ok...?

Answer 13

@Utterly_Confuzzled can you help me plz?

Answer 14

The surface area is the area of all the sides added up, so I believe you should just be able to take the surface area and divide it by 4 (since there's 4 sides) to get the area of one face.

2304 / 4 = 576 so, A, but I could be wrong because it's been forever since I've done any of these types of problems

Answer 15

@bohotness is correct.