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Answer:
The surface area of the pyramid in exact form is 64 + 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) =
∴ sin(60) =
- Multiply both sides by 8
∴ FE = 8 sin(60°)
∴ FE = 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 = × base × height
∵ AD is the base and FE is the height
∴ Area of each Δ = × 8 ×
∴ Area of each Δ = 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 ×
∴ Surface area of the pyramid = 64 +
The surface area of the pyramid in exact form is 64 + cm²
The approximated surface area of the pyramid is 174.9 cm²