Question

What is the surface area of this pyramid?

Answer 1

Answer:

Surface area of the given pyramid = 386.16 cm²

Step-by-step explanation:

Surface area of the given pyramid = Area of the square base + Area of the lateral sides

Area of the square base = (Side)²

                                        = (12)²

                                        = 144 cm²

Area of the lateral side = $\frac{1}{2}(\text{Base})(\text{Lateral height})$

Lateral height of the triangle = $\sqrt{6^2+(9.1)^2}$ [By applying Pythagoras theorem]

                                                = $\sqrt{82.81+36}$

                                                = $\sqrt{118.81}$

                                                = 10.9 cm

Area of the lateral side = $\frac{1}{2}(12)(10.9)$

                                      = 60.54 cm²

Surface area of the given pyramid = Area of the base + 4(Area of one lateral side)

                                                          = 144 + 4(60.54)

                                                          = 144 + 242.16

                                                          = 386.16 cm²