Question

Find the surface area of a rectangular pyramid with these measurements l=8 w=4 h=2

Answer 1

To find the surface area of a rectangular pyramid, we need to calculate the area of each of its faces and then sum them up.

Let's start with the base. The base of a rectangular pyramid is a rectangle. Given the length (l) and width (w) of the base, we can find its area:

Area of the base = l * w = 8 * 4 = 32 square units.

Now, let's calculate the area of the four triangular faces. Each triangular face has one side equal in length to the slant height of the pyramid (let's call it s), and the other two sides are equal in length to the base (l) and height (h) of the base. The slant height can be found using the Pythagorean theorem:

s = sqrt(l^2 + (0.5w)^2) = sqrt(8^2 + 2^2) = sqrt(64 + 4) = sqrt(68) = 2(sqrt(17))

Now we can calculate the area of each triangular face:

Area of one triangular face = 0.5 * l * s = 0.5 * 8 * 2(sqrt(17)) = 8(sqrt(17)) square units.

Since there are four triangular faces, the total area of the four triangular faces is:

Total area of four triangular faces = 4 * 8(sqrt(17)) = 32(sqrt(17)) square units.

Finally, to find the surface area of the rectangular pyramid, we add the area of the base and the area of the four triangular faces:

Surface area = Area of the base + Total area of four triangular faces = 32 + 32(sqrt(17)) square units.

Therefore, the surface area of the rectangular pyramid is 32 + 32(sqrt(17)) square units.