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

Answer 1

To find the surface area of a rectangular pyramid, we first need to find the areas of the different faces and then sum them up.

The area of the base is given by the formula A = l * w, where l represents the length and w represents the width. Plugging in the given values, we have A = 13cm * 11cm = 143cm^2.

The area of each triangular face is given by the formula A = 0.5 * l * h, where l represents the slant height and h represents the height of the triangle. In this case, the slant height can be found using the Pythagorean theorem: l = sqrt((0.5 * l)^2 + h^2). Plugging in the given values, we have l = sqrt((0.5 * 13cm)^2 + 8cm^2) = sqrt(84.25cm^2) ≈ 9.19cm (rounded to the nearest hundredth).

Now we can find the area of each triangular face: A = 0.5 * 9.19cm * 8cm = 36.76cm^2.

Since there are four triangular faces, the total area of the triangular faces is 4 * 36.76cm^2 = 147.04cm^2.

Finally, we can find the surface area by summing up the areas of the base and the triangular faces: SA = 143cm^2 + 147.04cm^2 = 290.04cm^2.

Therefore, the surface area of the rectangular pyramid is approximately 290.04 square centimeters.