Question

Find the surface area of a rectangular pyramid with these measurements: l
= 13 cm, w
= 11 cm, and h
= 8 cm. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
___ cm2

Answer 1

Base area = l·w = 13·11 = 143 cm².

Slant heights:
s_l = sqrt(h² + (w/2)²) = sqrt(8² + 5.5²) = sqrt(94.25) ≈ 9.70824 cm
s_w = sqrt(h² + (l/2)²) = sqrt(8² + 6.5²) = sqrt(106.25) ≈ 10.30776 cm

Lateral area = 2·(1/2·l·s_l) + 2·(1/2·w·s_w) = l·s_l + w·s_w
≈ 13(9.70824) + 11(10.30776) ≈ 239.59258 cm²

Total surface area = base + lateral ≈ 143 + 239.59258 = 382.59258 cm²

Rounded to the nearest hundredth: 382.59 cm².