Answer:
[tex]\boxed{\text{L = 90 in}^{2};\text{ S = 115 in}^{2}}[/tex]
Step-by-step explanation:
Data:
s = 5 in
l = 9 in
1. Lateral surface area
The general formula for the lateral surface area L of a regular pyramid is
L =½pl
where p represents the perimeter of the base and l the slant height.
The base is a square, so
p = 4 × 5 = 20 in
L = ½pl = ½ × 20 × 9 = [tex]\boxed{\text{90 in}^{2}}[/tex]
2. Total surface area
Total surface area = lateral surface area + area of base
S = L + B
B = b² = 5² = 25 in²
S = 90 + 25 = [tex]\boxed{\text{115 in}^{2}}[/tex]
