Answer to Question #148817 in Geometry for anlp

Question

A regular square pyramid has a height of 8m. If the slant height makes an angle of 45o with the base, find the lateral area of the pyramid

Answer 1

the height of regular square pyramid is that h = 8m

$\Alpha$ = 45^° is angle which between the slant height and base

l - is the slant height

l = h / sinA

a - the base of regular pyramid

a / 2 = h / tgA;

S - the literal area of regular pyramid

S = 2 * a * l = 2 * 2 * h / tgA * h / sinA = 4 * h² * cosA / sin²A =

= 4 * 64 * $\sqrt{2}$

S = 256 $\sqrt{2}$ ;