Answer:
[tex]1644.96in^2[/tex]
Step-by-step explanation:
The surface area of an equilateral triangular pyramid is given as:
[tex]S = A + \frac{3}{2}bh[/tex]
where
[tex]A = \sqrt{\frac{3}{4} }a^2[/tex] is the area of the pyramid's base
b = length of the base of one of the faces = 28 in
h = face height 23 in
The area of the base of the pyramid will be:
[tex]A = \sqrt{\frac{3}{4} }a^2[/tex][tex]= \sqrt{\frac{3}{4} } * 28^2[/tex]
[tex]A = 678.96 in^2[/tex]
Hence:
[tex]S = 678.96 + \frac{3}{2} * 28 * 23\\\\S = 678.96 + 966\\\\S = 1644.96in^2[/tex]
The surface area of the pyramid is [tex]1644.96in^2[/tex]
