Question

The Great Pyramid in Giza, Egypt, is a square pyramid. The dimensions of the pyramid at the time of its completion are shown in the net. What is the surface area of the Great Pyramid, including the base? Enter your answer in the box. 154 m² Shape made up of a square and four triangles the base of each triangle shared with each side of the square. The height of each triangle is 187 meters. The side of the square is 230 meters.

Answer 1

Answer:

Area of square pyramid is $153883.8\ m^{2}$.

Step-by-step explanation:

Diagram of the given scenario is shown below,

Given that,

The Great Pyramid in Giza, Egypt is a square pyramid. The area of base shape is made up with square is $154 \ m^{2}$. The side of the square is $230 \ m$ and The height of each triangle is $187 \ m$.

So,    Area of Square shape  = $154 \ m^{2}$

         Side of square = $230 \ m$

      Height of each triangle = $187 \ m$

Finding the Height of triangular shape which is here known as slant height.

 In Δ ABO, applying Right angle pythagorean Theorem,

                  Base $(BO)$ =  $\frac{230}{2} = 115\ m$

                Height $(AO)$ = $187\ m$

Now,      

∴                   $AB^{2} = AO^{2} \ + \ BO^{2}$

⇒                    $AB= \sqrt{AO^{2} \ + \ BO^{2} }$

⇒                   $AB= \sqrt{187^{2} \ + \ 115^{2} }$

⇒                   $AB= \sqrt{34969 \ + \ 13225 }$

⇒                   $AB= 219.53 \ m$

Then,

           Area of square pyramid = $area \ of \ square + \ 4\times area \ of \ traiangle$

                                                   = $side\times side + 4\times\frac{1}{2}\times AB\times Base$  

                                                   = $230\times 230 \ + 2\times 219.53\times 230$

                                                   = $52900 + 100983.8$

                                                   = $153883.8 \ m^{2}$

Hence, Area of square pyramid is $153883.8\ m^{2}$.