Answer:
s = 25.33m
θ = 60.65°
12.37m
A = 160m^2
Step-by-step explanation:
The pyramid has a side base of 35m and a height of 22m.
side base = b = 35m
height of the pyramid = h = 22m
To calculate the slant edge of the pyramid, you first calculate the diagonal of the squared base of the pyramid.
You use the Pythagoras theorem:
[tex]d=\sqrt{(\frac{35}{2})^2+(\frac{35}{2})^2}=24.74[/tex]
With the half of the diagonal and the height, and by using again the Pythagoras theorem you can calculate the slat edge:
[tex]s=\sqrt{(\frac{24.74}{2})^2+(22)^2}=25.23[/tex]
The slant edge of the pyramid is 25.33m
The angle of the base is given by:
[tex]\theta=sin^{-1}(\frac{h}{s})=sin^{-1}(\frac{22}{25.23})=60.65\°[/tex]
The angle of the base is 60.65°
The distance between the corner of the pyramid and its center of its base is half of the diagonal, which is 24.74/2 = 12.37m
The area of one side of the pyramid is given by the following formula:
[tex]A=\frac{(b/2)l}{2}[/tex] (1)
l: height of the side of pyramid
then, you first calculate l by using the information about the side base and the slant.
[tex]l=\sqrt{s^2-(\frac{b}{2}^2)}=\sqrt{(25.33)^2-(\frac{35}{2})^2}\\\\l=18.31m[/tex]
Next, you replace the values of l and b in the equation (1):
[tex]A=\frac{(35/2)(18.31)}{2}=160m^2[/tex]
The area of one aside of the pyramid is 160m^2
