Question

Find the surface area of the rectangle pyramid with these measurements left equals 13 cm, equals 11 cm and height equals 8 cm express your answer as a Decimal

Answer 1

Assuming a right rectangular pyramid with base sides 13 cm and 11 cm and vertical height 8 cm:

Half-sides: a = 13/2 = 6.5 cm, b = 11/2 = 5.5 cm.
Slant heights:
l1 = sqrt(8^2 + b^2) = sqrt(64 + 5.5^2) = sqrt(94.25) ≈ 9.7082439 cm (for the 13-cm sides),
l2 = sqrt(8^2 + a^2) = sqrt(64 + 6.5^2) = sqrt(106.25) ≈ 10.3077641 cm (for the 11-cm sides).

Lateral area = 2*(1/2*13*l1) + 2*(1/2*11*l2) = 13·l1 + 11·l2 ≈ 13(9.7082439) + 11(10.3077641) ≈ 239.5926 cm^2.
Base area = 13·11 = 143 cm^2.

Total surface area ≈ 143 + 239.5926 = 382.5926 cm^2.

Rounded to two decimals: 382.59 cm^2.