Answer:
The lateral height of the square pyramid is [tex]5.8\ ft[/tex]
Step-by-step explanation:
step 1
Find the surface area of the cube
The surface area of the cube is equal to
[tex]SA=6b^{2}[/tex]
where
b is the length side of the cube
w have
[tex]b=6\ ft[/tex]
substitute
[tex]SA=6(6^{2})=216\ ft^{2}[/tex]
step 2
Find the lateral height of the square pyramid
we know that
the surface area of the square pyramid is equal to
[tex]SA=B+4(\frac{1}{2}bh)[/tex]
where
B is the area of the base
b is the base of the lateral triangle (base of the square)
h is the lateral height of the square pyramid
[tex]B=(10^{2})=100\ ft^{2}[/tex]
[tex]SA=216\ ft^{2}[/tex] -----> is the same surface that the cube
[tex]b=10\ ft[/tex]
substitute the values and solve for h
[tex]216=100+4(\frac{1}{2}*(10)*h)[/tex]
[tex]216-100=20h[/tex]
[tex]h=116/20=5.8\ ft[/tex]
