Question

Help Me Please!!!

Answer 1

Answer:

The surface area is $288\ cm^{2}$

Step-by-step explanation:

we know that

The surface area of the square pyramid is equal to the area of the square base plus the area of its four triangular lateral faces

so

$SA=b^{2} +4[(\frac{1}{2}) (b)(h)]$

where

b is the length side of the square base

h is the height of each lateral triangular face

we know that

$\frac{b}{2}=h$ -----> by angle of 45 degrees

$sin(45\°)=\frac{h}{6\sqrt{2}}$

$h=6\sqrt{2}(sin(45\°)$

$h=6\ cm$

Find the value of b

$b=2h=2(6)=12\ cm$

Find the surface area

$SA=12^{2} +4[(\frac{1}{2}) (12)(6)]=288\ cm^{2}$