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24 May, 00:25

Find the total surface area of the following pyramids: A regular square pyramid has a height of 4 and a base with area 36.

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Answers (2)
  1. 24 May, 00:58
    0
    96 units²

    Step-by-step explanation:

    Base area = side² = 36

    Each side = 6 units

    Surface area includes 1 square and 4 identical slant triangles

    Area of square: 36

    height of a slant triangle:

    height² = 3² + 4² = 25

    height = 5

    Area of each slant triangle = ½*6*5 = 15

    Total SA = 36 + 4 (15)

    = 36 + 60 = 96 units²
  2. 24 May, 02:25
    0
    2623.6144m²

    Step-by-step explanation:

    Total Surface Area of a Square Pyramid

    a * (a + √ (a² + 4h²))

    where,

    a = area of base

    h = height

    Using the formula above

    a * (a + √ (a² + 4h²))

    data given:

    a = 36

    h = 4

    a * (a + √ (a² + 4h²))

    T. S. A. = a * (a + √ (a² + 4h²))

    Inputting values

    T. S. A. = 36 * (36 + √ (36² + 4 * 4²))

    T. S. A. = 36 * (36 + √ (36² + 4 * 16))

    T. S. A. = 36 * (36 + √ (36² + 64))

    T. S. A. = 36 * (36 + √ (1296 + 64))

    T. S. A. = 36 * (36 + √ (1360))

    T. S. A. = 36 * (36 + 36.87817782917154)

    T. S. A. = 36 * (72.87817782917154)

    T. S. A. = 36 * 72.8782

    T. S. A. = 2623.614401850175

    Therefore Total Surface Area (T. S. A.) is 2623.6144m²
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