10cm 10.6cm 14cm 12cm what is the sureface area of the rectangle pyramid
To calculate the surface area of a rectangular pyramid, we need to find the area of the base and add it to the area of the three triangular faces.
Given that the base of the pyramid is a rectangle with dimensions 10cm and 14cm, the area of the base is:
Area_base = Length * Width
Area_base = 10cm * 14cm
Area_base = 140 cm^2
Next, we need to find the area of the three triangular faces. The lateral faces of a rectangular pyramid are all identical, so we only need to calculate the area of one and then multiply by 3.
The formula for the area of a triangular face is given by:
Area_triangle = 0.5 * base * height
The base of the triangle is the same as the length of the rectangle base, which is 10cm. The height of the triangle is the slant height of the pyramid, which we can find using the Pythagorean theorem.
The slant height (l) can be calculated as:
l = sqrt(height^2 + (1/2 * length)^2)
l = sqrt(12^2 + (1/2 * 10)^2)
l = sqrt(144 + 25)
l = sqrt(169)
l = 13 cm
Now we can calculate the area of one triangular face:
Area_triangle = 0.5 * 10cm * 13cm
Area_triangle = 65 cm^2
Finally, we find the total surface area of the rectangular pyramid by adding the base area and the area of the three triangular faces:
Surface Area = Area_base + 3*Area_triangle
Surface Area = 140 cm^2 + 3(65 cm^2)
Surface Area = 140 cm^2 + 195 cm^2
Surface Area = 335 cm^2
Therefore, the surface area of the rectangular pyramid is 335 cm^2.