Find the surface area of a rectangular pyramid with these measurements: Length = 13, width = 11, and height = 8. Express your answer as a decimal rounded to the nearest hundredth.

1 answer

To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of each face.

The base of the pyramid is a rectangle with dimensions 13 and 11. So, the area of the base is $13 \cdot 11 = 143$.

Now, we need to find the area of each face. The four triangular faces will have the same area, so we can find the area of one and multiply by 4.

To find the area of one triangular face, we can use the formula for the area of a triangle:

$\frac{1}{2} \cdot \text{base} \cdot \text{height}$.

The base of each triangular face is 11, and the height of each triangular face is 8. So, the area of one triangular face is $\frac{1}{2} \cdot 11 \cdot 8 = 44$.

Since there are four triangular faces, the total area of the four triangular faces is $4 \cdot 44 = 176$.

Finally, we can find the surface area of the rectangular pyramid by adding the area of the base and the area of the four triangular faces: $143 + 176 = 319$.

Therefore, the surface area of the rectangular pyramid is 319. Answer: \boxed{319}.