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

66 yd.2

66 yd. power 2

43.31 yd.2

43.31 yd. power 2

72.52 yd.2

72.52 yd. power 2

55.55 yd.2

Answer 1

Surface area = base + 4 triangular faces
Base = l·w = 8·4 = 32 yd^2.

Slant heights:
s_l = sqrt(h^2 + (w/2)^2) = sqrt(2^2 + 2^2) = sqrt(8) = 2√2 ≈ 2.8284 yd
s_w = sqrt(h^2 + (l/2)^2) = sqrt(2^2 + 4^2) = sqrt(20) = 2√5 ≈ 4.4721 yd

Total lateral area = l·s_l + w·s_w = 8(2.8284) + 4(4.4721) ≈ 22.627 + 17.889 = 40.516 yd^2

Surface area ≈ 32 + 40.516 = 72.516 ≈ 72.52 yd^2.

Answer: 72.52 yd^2.