Answer:
The surface area of the pyramid in exact form is 64 + [tex]64\sqrt{3}[/tex] cm²
The approximated surface area of the pyramid is 174.9 cm²
Step-by-step explanation:
The surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces
In Δ EFD
∵ m∠EFD = 90°
∵ m∠FDE = 60°
∵ ED = 8 cm
- By using sine ratio to find FE
∵ sin(∠FDE) = [tex]\frac{FE}{ED}[/tex]
∴ sin(60) = [tex]\frac{FE}{8}[/tex]
- Multiply both sides by 8
∴ FE = 8 sin(60°)
∴ FE = [tex]4\sqrt{3}[/tex] cm
In Δ AED
∵ AE = ED
∵ m∠D = 60°
- In any isosceles Δ if measure of an angle is 60, then the
triangle is equilateral Δ
∴ Δ AED is an equilateral Δ
∴ AD = 8 cm
∵ The pyramid has 4 identical triangular faces
∵ Area of each Δ = [tex]\frac{1}{2}[/tex] × base × height
∵ AD is the base and FE is the height
∴ Area of each Δ = [tex]\frac{1}{2}[/tex] × 8 × [tex]4\sqrt{3}[/tex]
∴ Area of each Δ = [tex]16\sqrt{3}[/tex] cm²
∵ Surface area of the pyramid = Area of base + 4 area of a Δ
∵ Area of base = 8²
∴ Area of base = 64 cm²
∴ Surface area of the pyramid = 64 + 4 × [tex]16\sqrt{3}[/tex]
∴ Surface area of the pyramid = 64 + [tex]64\sqrt{3}[/tex]
The surface area of the pyramid in exact form is 64 + [tex]64\sqrt{3}[/tex] cm²
The approximated surface area of the pyramid is 174.9 cm²
