Answer:
Surface area of the pyramid = 157.99 in²
Step-by-step explanation:
Volume of a pyramid is given by the formula,
Volume = [tex]\frac{1}{3}(\text{Area of the base})\times \text{height}[/tex]
100 = [tex]\frac{1}{3}\text{(Side)}^{2} \times \text{height}[/tex]
300 = s² × 5
s² = 60
s = √60
s = 2√15 in ≈ 7.746 in
Now surface area of the pyramid = Area of base + 4×(Area of one lateral side)
Area of square base = (Side)² = 60 in
Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]
Since Lateral height = [tex]\sqrt{(h)^{2}+(\frac{S}{2})^{2}}[/tex] [By applying Pythagoras theorem in the given triangle]
= [tex]\sqrt{(5)^{2}+(3.873)^{2}}[/tex]
= [tex]\sqrt{25+15}[/tex]
= [tex]\sqrt{40}[/tex]
= 6.325 in.
Now area of lateral side = [tex]\frac{1}{2}(7.746)(6.325)[/tex]
= 24.497 in²
Surface area of the pyramid = 60 + (4×24.497)
= 60 + 97.987
= 157.987 in²
≈ 157.99 in²
