Question

what is the slant height for the given pyramid to the nearest whole unit? with a pyramid base of 12cm and a height of 8cm. MY ANSWER: 14

Answer 1

Interpretation #1 : Slant height is the edge of the pyramid

Consider the right-angled (internal) triangle formed by the height , half the diagonal of the base and hypotenuse being the slant height.

let the slant height be x

let the diagonal of the base be d
d^2 = 1^2 + 12^2 = 288
d^2 = 288
d = 12√2
d/2 = 6√2

then x^2 = (d/2)^2 + 8^2 = 72 + 64 = 136
x+ √136 = 2√34 or appr 11.66



Interpretation #2 : slant height is the altitude of one of the triangles:



Consider one of the triangles whose base runs from the centre of the pyramid to the midpoint of a base side, with height 8 and hypotenuse as your "slant height"
base = 6
slant height = hypotenuse = y
height =8

where y^2 = 8^2 + 6^2 = 100
y = √100 = 10



Check: notice I can obtain the edge length from this as well

x^2 = y^2 + 6^2
x^2 = 100+36 = 136
x = √136 (same as above)

Answer 2

thank you!