A pyramid with a square base has a height of 10 and a slant height of 26. What is the volume and surface area of the pyramid?

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Answer 1 · 2017-12-06T05:27:58

L S A = 2496

T S A = 4800

Volume = 7680

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Square pyramid height h = 10 and slant height l = 26
Let b be the side of the base square.

#:. b/2 = sqrt(26^2 - 10^2) = sqrt 576 = 24#
#b = 48#

Base square area = #b^2 = 48^2 = **2304 **#

Lateral surface area #L S A = 4 * (1/2) * b * l = 4*(1/2)*48*26 = **2496** #

Total Surface Area #T S A = 2304 + 2496 = color(red)(4800)#

Volume #V = (1/3)* b^2 * h = (1/3) * 2304 * 10 = color(purple)(7680)#