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
A rectangular pyramid has a triangular base and four triangular faces.
To find the area of the base, we can use the formula for the area of a triangle: (1/2) * base * height. The base of the triangle is one of the sides of the pyramid, which is given as 11 cm. The height of the triangle is the height of the pyramid, which is given as 8 cm.
Area of the base = (1/2) * 11 cm * 8 cm = 44 cm^2.
To find the area of one of the triangular faces, we need to find the slant height of the triangle. The slant height can be found using the Pythagorean theorem. The base of the triangle is the same as the base of the pyramid, which is given as 11 cm. The height of the triangle is the height of the pyramid, which is given as 8 cm. The slant height, labeled "l" in the diagram, can be found using the equation l = sqrt((base/2)^2 + height^2).
l = sqrt((11/2)^2 + 8^2) = sqrt(30.25 + 64) = sqrt(94.25) ≈ 9.71 cm.
Now that we have the slant height, we can find the area of one triangular face using the formula: (1/2) * base * height. The base of the triangle is the same as the base of the pyramid, which is given as 11 cm. The height of the triangle is the slant height, which we just found as approximately 9.71 cm.
Area of one triangular face = (1/2) * 11 cm * 9.71 cm = 53.405 cm^2.
Since there are four triangular faces, the total area of the four triangular faces is 4 * 53.405 cm^2 = 213.62 cm^2.
Finally, to find the total surface area of the pyramid, we can add the area of the base to the area of the four triangular faces.
Total surface area = Area of the base + Area of the four triangular faces
= 44 cm^2 + 213.62 cm^2
= 257.62 cm^2.
Therefore, the surface area of the rectangular pyramid is approximately 257.62 cm^2.