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?

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Answer 1 · 2018-07-25T12:18:12

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

Area of one triangular face $= 21 sft$

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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,

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

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

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

$h = sqrt(40)’ ~~ 6.3246’$