Question

Find the surface area of a rectangular pyramid with these measurements: l
= 8 yd., w
= 4 yd., and h
= 2 yd.(1 point)
Responses

43.31 yd.2

43.31 yd. power 2

72.52 yd.2

72.52 yd. power 2

66 yd.2

66 yd. power 2

55.55 yd.2

Answer 1

Surface area = base area + lateral area.

Base area = l·w = 8·4 = 32 yd^2.

Slant heights:
- for faces with base 8: s1 = sqrt(h^2 + (w/2)^2) = sqrt(2^2 + 2^2) = sqrt(8) ≈ 2.8284 yd
- for faces with base 4: s2 = sqrt(h^2 + (l/2)^2) = sqrt(2^2 + 4^2) = sqrt(20) ≈ 4.4721 yd

Lateral area = 2*(1/2·8·s1) + 2*(1/2·4·s2) = 8·s1 + 4·s2 ≈ 22.6274 + 17.8885 = 40.5160 yd^2.

Total surface area ≈ 32 + 40.516 = 72.52 yd^2.

Answer: 72.52 yd^2.