Triangular pyramid B is the image of triangular pyramid A after dilation by a scale factor of 33. If the surface area of triangular pyramid A is 55in2, find the surface area of triangular pyramid B, the image.
Q. Triangular pyramid B is the image of triangular pyramid A after dilation by a scale factor of 33. If the surface area of triangular pyramid A is 55in2, find the surface area of triangular pyramid B, the image.
Cube Scale Factor: Since the scale factor for the dilation is 33, we need to cube this scale factor to find the change in surface area because surface area is a two-dimensional measurement and dilation affects each dimension of the shape.
Calculate New Surface Area: Calculate the new surface area by cubing the scale factor: 333=35,937.
Multiply Original Surface Area: Multiply the original surface area of triangular pyramid A by the cubed scale factor to get the surface area of triangular pyramid B: 55 in2×35,937.