Find the surface area of a rectangular pyramid with these measurements: length = 13 cm, width = 11 cm, and height = 8 cm. Express your answer as a decimal rounded to the nearest hundredth.
A rectangular pyramid has a rectangular base and four triangular faces. The surface area of a pyramid is given by the formula $B+\frac{1}{2}Pl$, where $B$ is the area of the base, $P$ is the perimeter of the base, and $l$ is the slant height of a face.
The base of the pyramid is a rectangle with dimensions $13\text{ cm}\times 11\text{ cm}$, so its area is $(13)(11)=143$ square cm.
The perimeter of the base is $2(13)+2(11)=48$ cm.
The slant height of the triangular faces can be found using the Pythagorean Theorem. Consider the right triangle formed by the height, the slant height, and one-half the length of the base of the triangle. The hypotenuse has length 11 cm, one of the legs has length 8 cm, and we need to find the length of the other leg which is the slant height of the triangular face. Using the Pythagorean Theorem, we get $l^2=11^2-8^2=15^2$, so $l=15$.
The surface area of the pyramid is $B+\frac{1}{2}Pl=143+\frac{1}{2}(48)(15)=143+12(15)=143+180=\boxed{323}$ square cm.