find the surface area of a rectangular pyramid with these measurements: I = 8 cm, w = 4 cm, and h = 2 cm. express your answer as a decimal rounded to the nearest hundredth.
To find the surface area of a rectangular pyramid, we need to find the area of each face and add them together.
First, let's find the area of the base. The base of a rectangular pyramid is a rectangle, therefore, the area of the base is length * width. Using the given dimensions, the base area is 8 cm * 4 cm = 32 cm².
Next, let's find the area of the four triangular faces. The formula for the area of a triangle is 1/2 * base * height. The base of each triangular face is a side of the rectangular base, which is 4 cm. The height of each triangular face is the slant height of the pyramid, which can be found using the Pythagorean theorem.
The slant height of the pyramid is given by:
slant height = √(height² + (1/2 * base)²)
slant height = √(2 cm² + (1/2 * 4 cm)²)
slant height = √(2 cm² + 2 cm²)
slant height = √(4 cm²)
slant height = 2 cm
Now we can find the area of each triangular face:
Area of each triangular face = 1/2 * base * height
Area of each triangular face = 1/2 * 4 cm * 2 cm
Area of each triangular face = 4 cm²
There are four triangular faces, so the total area of all four triangular faces is 4 * 4 cm² = 16 cm².
Finally, we can find the total surface area of the pyramid by adding the area of the base and the area of the four triangular faces:
Total surface area = base area + area of four triangular faces
Total surface area = 32 cm² + 16 cm²
Total surface area = 48 cm²
Therefore, the surface area of the rectangular pyramid is 48 cm² rounded to the nearest hundredth.