Here is a square pyramid and its net. The lateral faces are congruent triangles. The base (shaded) is a square.
(All lengths are in centimeters.)

A. Find the area of the base of the pyramid.
B. Find the area of one lateral face of the pyramid
C. Use the net to find the lateral surface area of the pyramid. The base is not included.
D. Use the net to find the total surface area of the pyramid.

A. 9

B. 9.6

C. 38.4

D. 47.4

Step-by-step explanation:

A. Area of the base of the pyramid = length x length

                                               = 3 x 3

                                               = 9

B. Area of one lateral face of the pyramid = area of a triangle

                                                = x base x height

                                                = x 3 x 6.4

                                                = 9.6

Area of one lateral face of the pyramid  = 9.6

C. The lateral surface area of the pyramid =  4 x area of one lateral face

                                                  = 4 x 9.6

                                                  = 38.4

The lateral surface area of the pyramid =  38.4

D. The total surface area of the pyramid = lateral surface area of the pyramid +  area of the base

                                                  = 38.4 + 9

                                                  = 47.4

The total surface area of the pyramid = 47.4