Answer:
To calculate the surface area of a rectangular pyramid, you need to find the area of each face and then sum them up.
Given the dimensions:
- Base length: 10 cm
- Base width: 10.6 cm
- Height of the pyramid: 12 cm
Let's break down the faces:
1. The base area is length times width: \(10 \times 10.6 = 106 \, \text{cm}^2\).
2. Each of the triangular faces has a base of 10 cm and a height of 12 cm (using the height of the pyramid). The formula for the area of a triangle is 1/2 base times height, so each triangular face has an area of \(0.5 \times 10 \times 12 = 60 \, \text{cm}^2\).
3. There are four triangular faces in total, so their combined area is \(4 \times 60 = 240 {cm}^2
Now, summing up all the areas:
\[ \text{Surface Area} = \text{Base area} + \text{Area of triangular faces}
\[ \text{Surface Area} = 106 \, \text{cm}^2 + 240 \, \text{cm}^2 = 346 cm^2
So, the surface area of the rectangular pyramid is \(346 \, \text{cm}^2\).
