Answer:
Area of square pyramid is [tex]153883.8\ m^{2}[/tex].
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 [tex]154 \ m^{2}[/tex]. The side of the square is [tex]230 \ m[/tex] and The height of each triangle is [tex]187 \ m[/tex].
So, Area of Square shape = [tex]154 \ m^{2}[/tex]
Side of square = [tex]230 \ m[/tex]
Height of each triangle = [tex]187 \ m[/tex]
Finding the Height of triangular shape which is here known as slant height.
In Δ ABO, applying Right angle pythagorean Theorem,
Base [tex](BO)[/tex] = [tex]\frac{230}{2} = 115\ m[/tex]
Height [tex](AO)[/tex] = [tex]187\ m[/tex]
Now,
∴ [tex]AB^{2} = AO^{2} \ + \ BO^{2}[/tex]
⇒ [tex]AB= \sqrt{AO^{2} \ + \ BO^{2} }[/tex]
⇒ [tex]AB= \sqrt{187^{2} \ + \ 115^{2} }[/tex]
⇒ [tex]AB= \sqrt{34969 \ + \ 13225 }[/tex]
⇒ [tex]AB= 219.53 \ m[/tex]
Then,
Area of square pyramid = [tex]area \ of \ square + \ 4\times area \ of \ traiangle[/tex]
= [tex]side\times side + 4\times\frac{1}{2}\times AB\times Base[/tex]
= [tex]230\times 230 \ + 2\times 219.53\times 230[/tex]
= [tex]52900 + 100983.8[/tex]
= [tex]153883.8 \ m^{2}[/tex]
Hence, Area of square pyramid is [tex]153883.8\ m^{2}[/tex].
