Respuesta :
Answer:
The slant height is 9 meters.
Step-by-step explanation:
To determine the slant height, we will follow the steps below;
First, write down the formula:
Surface area = 2bs + b²
where b= the length of the base of the square pyramid
s = the slant height of the square pyramid
From the question given,
surface area of a square pyramid = 360 square meters
base length = 12 meters
We can now proceed to insert the values into the formula and then solve for s
Surface area = 2bs + b²
360 = 2(12)s + (12)²
360 = 24s + 144
subtract 144 from both-side of the equation
360 - 144 = 24s
216 = 24s
Divide both-side of the equation by 24
216/24 = 24s/24
9 = s
s = 9 meters
The slant height is 9 meters.
Answer:
The slant height is [tex]l=9 \:m[/tex].
Step-by-step explanation:
A regular pyramid is a pyramid where the base is a regular polygon.
The surface area of a regular pyramid is given by
[tex]SA=B+\frac{1}{2} nbl[/tex]
where, [tex]B[/tex] is the area of the base, [tex]n[/tex] is the number of triangles, [tex]b[/tex] is base length, and [tex]l[/tex] is the slant height.
A square pyramid is a pyramid having a square base.
From the information given we know that is a square pyramid ([tex]n =4[/tex]), the surface area is 360 [tex]m^2[/tex] and the base length is 12 [tex]m[/tex].
The area of the base is given by
[tex]B=l^2\\\\B=12^2=144[/tex]
Applying the equation for the surface area and solving for the slant height, we get that
[tex]SA=B+\frac{1}{2} nbl\\\\360=144+\frac{1}{2} 4\cdot 12\cdot l\\\\144+\frac{1}{2}\cdot \:4\cdot \:12l=360\\\\144+24l=360\\\\24l=216\\\\\frac{24l}{24}=\frac{216}{24}\\\\l=9[/tex]
The slant height is [tex]l=9 \:m[/tex].
