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

72.52 yd.2
72.52 yd. power 2

43.31 yd.2
43.31 yd. power 2

55.55 yd.2

Answer 1

Surface area = base + lateral faces.

Base area = l·w = 8·4 = 32 yd².

Slant heights:
- for the faces with base 8: s1 = sqrt(h² + (w/2)²) = sqrt(2² + 2²) = sqrt(8) = 2√2 ≈ 2.8284
- for the faces with base 4: s2 = sqrt(h² + (l/2)²) = sqrt(2² + 4²) = sqrt(20) = 2√5 ≈ 4.4721

Lateral area = l·s1 + w·s2 = 8·(2√2) + 4·(2√5) = 16√2 + 8√5 ≈ 40.516

Total surface area ≈ 32 + 40.516 = 72.52 yd².

So the correct choice is 72.52 yd².