In a rectangular pyramid, the area of one triangular face is 21 square ft (it also has a height of 7 ft). What is the height of the pyramid?

1 Answer
Kalyanam S.
Jul 25, 2018

Height of pyramid #color(purple)(h = sqrt 40’ ~~ 6.3246’#

Explanation:

Area of one triangular face # = 21 sft#

https://socratic.org/questions/a-pyramid-has-a-parallelogram-shaped-base-and-a-peak-directly-above-its-center-i-123

Let Base of triangle as #x#. Triangle’s height #s = 7’#

#:. (1/2) * x * 7 = 21# or #x = 6’#

Let height of pyramid be #h#

Applying Pythagoras theorem,

#((x/2)^2 + h^2) = s^2#

#(6/2)^2 + h^2 = 7^2#

#h^2 = 7^2 - 3^2 = 40#

#h = sqrt(40)’ ~~ 6.3246’#

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