Question

The shaded area in the diagram below shows the cross section of a pyramid intersected by a plane that passes through the apex and is perpendicular to the base. The base of the pyramid is a square of side 16 cm. Each edge of the triangular faces is 24 cm long.



Which is the best approximation of the perimeter of the cross section?

61 cm

40 cm

52 cm

39 cm

Answer 1

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_Seg_Two_Exam_63/image0014e9daea7.jpg

Answer 2

http://www.mathsteacher.com.au/year7/ch13_area/04_triangle/right.htm

Answer 3

Um.....

Answer 4

Ok, thanks!!!

Answer 5

but the answer I get is not in one of the options....

Answer 6

c= 320
c= 17.89

Answer 7

In order to find the area of the right triangle, we need the base and height. The given, however, are only the hypotenuse and the base. We can make use of pythagorean theorem to find "opposite side" or the height.
\[c^2−a^2=b^2\]

\[24^2−16^2=b^2\]

solve for b, that is the square root of the above problem (c^2) .

since the value of b is the "height" of the triangle, now we can use the formula
\[\frac{ 1 }{ 2 }(b \times h)\]

Answer 8

sorry, I keep typing c^2... it's square root of the b^2

Answer 9

ok, so 1/2 ( 16 x 17.89) ?

Answer 10

yes, what do you get?

Answer 11

Which gets me 143.12. Which isn't one of my answer choices.

Answer 12

......

Answer 13

yeah.... so, now what should we do?

Answer 14

let me write it down myself

Answer 15

ok.

Answer 16

I found out where I made a mistake.

Answer 17

Ok. So what would be the correct way to figure this out?

Answer 18

Pretty please, pan?

Answer 19

@panlac01 ^^^^

Answer 20

we have been looking for area, but the problem is looking for perimeter LOL

Answer 21

XD

Answer 22

so Pythagorean theorem, and add up the sides?

Answer 23

\[P=24+24+16\]

Answer 24

are you sure that one of the option is 61, not 64?

Answer 25

P=64

Answer 26

Yes, I am sure

Answer 27

it says so on my assignment.

Answer 28

just add up the sides, no pythagorean theorem

Answer 29

I got 64

Answer 30

but the option says 61

Answer 31

Should I just go with 61?

Answer 32

yeh

Answer 33

Ok, thanks pan! :)

Answer 34

cross your finger that it is the right answer

Answer 35

;)
I will. And I just might inform the teacher, so I can get credit for that question.