What is the slant of a square pyramid that has a surface area of 336 square meters and a side length of 12 meters

Answer 1

surface area = 336 = 4 times x (x=the surface area of each of 4 sides)

x=336/4= 84

each of the surface areas of the sides = one half times the base 12 times the slanted height.

Area of each = 84 = (1/2)12y where y= slanted height

y= 84/6 = 14 feet

each of the four sides form triangles 14 x 14 x12

the center of the bottom of the pyramid is half way, in the middle, a distance of 6 from the base on any of the 4 sides. This forms an upright right triangle of 6 x 14 x sqr(14^2 - 6^2) = 6x14xsqr160=6x14x4sq10=6x14x12.64

the slant is the angle formed between the base 6 and the side 14 which is the angle whose cosine = 6/14=3/7

Use the inverse trig function on a calculator to get about 64.6 degrees or a little over pi/3=60 degrees

Answer 2

s represents the side length

The area of each face is (0.5)(12)(s)

The area of the four sides (surface area) is (4)(0.5)(12)(s)

336 = (4)(0.5)(12)(s)

Can you solve for s and answer?