The surface area of a square pyramid 360 square meters. The base length is 12 meters. Determine the slant height.

Question

The surface area of a square pyramid 360 square meters. The base length is 12 meters. Determine the slant height.

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Liliana 2 weeks 2021-10-06T06:18:41+00:00 2 Answers 0

Answers ( )

    0
    2021-10-06T06:20:15+00:00

    Answer:

    The slant height is l=9 \:m.

    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

                                                       SA=B+\frac{1}{2} nbl

    where, B is the area of the base, n is the number of triangles, b is base length, and l 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 (n =4), the surface area is 360 m^2 and the base length is 12 m.

    The area of the base is given by

    B=l^2\\\\B=12^2=144

    Applying the equation for the surface area and solving for the slant height, we get that

    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

    The slant height is l=9 \:m.

    0
    2021-10-06T06:20:15+00:00

    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.

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