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11 October, 15:19

The sides of the base of a right Square pyramid are 3 Meters in length, And it's slant height is 6 m. If the length of the side of the base and the slant height are each multiplied by 3, by what factor is the surface area X?

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  1. 11 October, 15:39
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    9

    Step-by-step explanation:

    We have that the total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base, therefore, it would be equal to:

    As = 1/2 * p * h + l ^ 2

    where l are the sides that measure 3, p is the perimeter that is the sum of the sides, and since there are 4 sides, then it would be 12 (3 * 4), h the inclined height is 6, replacing we are left with:

    As = 1/2 * 12 * 6 + 3 ^ 2

    Ace = 45

    Now they say the sides and the tilt height are multiplied by 3, the sides now measure 9, therefore the perimeter is 36 (4 * 9), the height would be 18, the replacement would be:

    Ace = 1/2 * 36 * 18 + 9 ^ 2

    Ace = 405

    Therefore, the factor would be:

    405/45 = 9

    Which means that the factor is 9.
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