Question

A regular square pyramid has an altitude of 15 m and volume of 125 m3.
1. What is the base edge of a square pyramid?
2. What is the slant height of the pyramid?
3. What is the lateral area in m2?

Answer 1

$1.$ $V=1/3a^2h; a=\sqrt{\smash[b]{3V/h}}; a=\sqrt{\smash[b]{3*125/5}}=5m;$

$2.$

$SOK: SO=15m; OK=a/2=2.5; SK=\sqrt{\smash[b]{OK^2+SO^2}}; \\SK=\sqrt{\smash[b]{6.25+225}}=\sqrt{\smash[b]{231.25}}=5\sqrt{\smash[b]{9.25}};$

$3. L.A.= 1/2SK*P; P=4a=4*5=20; \\ L.A.=1/2*5\sqrt{\smash[b]{9.25}}*20=50\sqrt{\smash[b]{9.25}}m^3.$