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:
s1 (for side 8) = sqrt(h² + (w/2)²) = sqrt(2² + 2²) = sqrt8 = 2√2 ≈ 2.828427.
s2 (for side 4) = 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) = 8·s1 + 4·s2
≈ 8·2.828427 + 4·4.472136 ≈ 22.627416 + 17.888544 = 40.515960.

Total surface area = 32 + 40.515960 ≈ 72.51596 ≈ 72.52 cm² (to nearest hundredth).