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 22 cm. Each edge of the triangular faces is 15 cm long.

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

Answer 1

31 cm
35 cm
42 cm
52 cm

Answer 2

you're missing the diagram

Answer 3

:)

Answer 4

thanks

Answer 5

The base of that shaded triangle is 22 cm since it's parallel to that length, can you see this?

Answer 6

yes each side of the base is 22 cm right

Answer 7

you got it

Answer 8

The slant height of the pyramid is all we need now. So let's find it. Let's use the Pythagorean theorem to do that.


a^2 + b^2 = c^2


11^2 + b^2 = 15^2


121 + b^2 = 225


b^2 = 225-121


b^2 = 104


b = sqrt(104)


So the exact length of the slant height is sqrt(104)


So the perimeter of this shaded triangle is


P = sqrt(104)+sqrt(104)+22


P = 10.198039+10.198039+22


P = 42.396078


Which rounds to 42 cm


So it's choice C

Answer 9

Thank you so much, I had no Idea where to go with it!

Answer 10

I'm glad I could help