To find the surface area of a rectangular pyramid, we need to find the lateral area and the area of the base.
The lateral area can be found by multiplying the perimeter of the base by half of the slant height.
The perimeter of the base is 2(L+W), so it is 2(13+11) = 2(24) = 48 cm.
The slant height can be found using the Pythagorean theorem.
The slant height (s) is the square root of ( L/2 squared + H squared).
Substituting in the values, we have s = √((13/2)^2 + 8^2) = √(169/4 + 64) = √(169+256)/4 = √(425)/2.
Therefore, half of the slant height is √(425)/2.
The lateral area is the product of the perimeter of the base and half of the slant height, so it is 48*(√(425)/2) = 24√(425) cm.
The area of the base is L*W, so it is 13*11 = 143 cm^2.
The total surface area is the sum of the lateral area and the area of the base. So it is 24√(425) + 143 cm^2.
Rounded to the nearest hundredth, the surface area is approximately 256.36 cm^2.
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 answer