To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of each lateral face.
1. Area of the base:
The area of a rectangle is given by length * width. In this case, the length is 14 cm and the width is 12 cm, so the area of the base is 14 * 12 = 168 square cm.
2. Area of each lateral face:
The area of a triangle is given by 0.5 * base * height. Since the base of each lateral face is the same as the base of the pyramid (14 cm), we can calculate the area of each lateral face using the given perpendicular height:
- For the lateral face perpendicular to the length of 14 cm: 0.5 * 14 * 10 = 70 square cm
- For the lateral face perpendicular to the width of 12 cm: 0.5 * 12 * 10.6 = 63.6 square cm
3. Total surface area:
To find the total surface area, we sum the area of the base and the areas of the two lateral faces:
168 (base) + 70 (lateral face 1) + 63.6 (lateral face 2) = 301.6 square cm
Therefore, the surface area of the rectangular pyramid is 301.6 square cm.