Find the surface area of a rectangular pyramid with these measurements length equals 13 cm with equals 11 cm and height equals 8 cm expressed your answer as it 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 then sum them together.
First, let's find the area of the base. Since the base is a rectangle, we can calculate its area by multiplying the length and width. In this case, the length is 13 cm and the width is 11 cm. So, the area of the base is 13 cm * 11 cm = 143 cm².
Next, let's find the area of each triangular face. Since the pyramid is rectangular, it has four triangular faces. The formula for the area of a triangle is (1/2) * base * height.
For the first face, the base is the length of the rectangle (13 cm) and the height is the height of the pyramid (8 cm). So, the area of the first triangular face is (1/2) * 13 cm * 8 cm = 52 cm².
For the second face, the base is the width of the rectangle (11 cm) and the height is the height of the pyramid (8 cm). So, the area of the second triangular face is (1/2) * 11 cm * 8 cm = 44 cm².
Since the pyramid is rectangular, the third and fourth triangular faces will have the same areas as the first and second faces, respectively. So, the area of the third and fourth triangular faces is also 52 cm² and 44 cm², respectively.
Now, let's sum up the areas of all the faces to find the total surface area.
Total surface area = area of base + area of first face + area of second face + area of third face + area of fourth face
= 143 cm² + 52 cm² + 44 cm² + 52 cm² + 44 cm²
= 335 cm²
Therefore, rounded to the nearest hundredth, the surface area of the rectangular pyramid is 335 cm².