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

Surface area = base area + lateral area.

Base = 13·11 = 143 cm^2.

Slant heights:
s1 = sqrt(8^2 + (11/2)^2) = sqrt(94.25) ≈ 9.70825 cm
s2 = sqrt(8^2 + (13/2)^2) = sqrt(106.25) ≈ 10.30776 cm

Lateral area = 2*(1/2·13·s1) + 2*(1/2·11·s2)
= 13·s1 + 11·s2 ≈ 13·9.70825 + 11·10.30776 ≈ 239.59 cm^2

Total surface area ≈ 143 + 239.59 = 382.59 cm^2.

Answer: 382.59 cm^2.