Question

PLEASE HELP!!!!

Answer 1

Answer:

The surface area of the pyramid in exact form is 64 +  $64\sqrt{3}$ 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) = $\frac{FE}{ED}$

∴ sin(60) = $\frac{FE}{8}$

- Multiply both sides by 8

∴ FE = 8 sin(60°)

∴ FE = $4\sqrt{3}$ 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 = $\frac{1}{2}$ × base × height

∵ AD is the base and FE is the height

∴ Area of each Δ = $\frac{1}{2}$ × 8 ×  $4\sqrt{3}$

∴ Area of each Δ = $16\sqrt{3}$ 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 × $16\sqrt{3}$

∴ Surface area of the pyramid = 64 +  $64\sqrt{3}$

The surface area of the pyramid in exact form is 64 +  $64\sqrt{3}$ cm²

The approximated surface area of the pyramid is 174.9 cm²