Question

What is the slant height x of this square pyramid?

Answer 1

1) What is the slant height x of this square pyramid? Express your answer in radical form

sin 60=x/4--------> x=4*sin 60------> 4*(√3/2)-------> 2 √3 m

the answer Part 1) is 2 √3 m

2) The base of a regular pyramid is a hexagon. What is the area of the base of the pyramid?
[area of the base}=[area of hexagon]
[area of hexagon]=6*[area of triangle]

area of triangle
sin 60=a/14-------> a=(√3/2)*14-------> a=7√3 cm
cos 60=(b/2)/14--------> (b/2)=cos 60*14-----> (1/2)*14---------> (b/2)=7
base of triangle=2*7--------> b=14 cm

[area of triangle]=14*7√3 /2--------> 49√3 cm²
so
[area of hexagon]=6*[49√3]--------> 294√3 cm²