Question

Find the surface area of a rectangular pyramid with these measurements: l
= 8 cm, w
= 4 cm, and h
= 2 cm. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
cm2

Answer 1

Base area = 8·4 = 32 cm².

Slant heights:
- along length: s1 = sqrt(h² + (w/2)²) = sqrt(2² + 2²) = sqrt8 = 2√2 ≈ 2.828427
- along width: s2 = sqrt(h² + (l/2)²) = sqrt(2² + 4²) = sqrt20 = 2√5 ≈ 4.472136

Lateral area = 2·(1/2·8·s1) + 2·(1/2·4·s2)
= 2·(4·s1) + 2·(2·s2) = 8s1 + 4s2 ≈ 8(2.828427) + 4(4.472136) ≈ 40.51596

Total surface area ≈ 32 + 40.51596 = 72.51596 ≈ 72.52 cm².