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13 August, 20:59

A rectangular prism has a base length of 6 units, base

width of 5 units, and height of 4 units. The bases are

shaded.

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Answers (1)
  1. 13 August, 21:16
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    Your question is incomplete, the complete question is here

    A rectangular prism has a base length of 6 units, base width of 5 units, and height of 4 units. The bases are shaded.

    The lateral area is

    The area of the two bases together is

    The total surface area is

    Answer:

    The lateral area is 88 units²

    The area of the two bases together is 60 units²

    The total surface area is 148 units²

    Step-by-step explanation:

    The lateral area of a rectangular prism is the sum of the areas of the side faces

    The formula of the lateral area of a rectangular prism is LA = perimeter of its base (p) * its height (h)

    The formula of the total surface area of it is SA = LA + area of its two bases

    ∵ The rectangular prism has a base length of 6 units, base

    width of 5 units, and height of 4 units

    ∴ l = 6 units

    ∴ w = 5 units

    ∴ h = 4 units

    ∵ The dimensions of the base area the length and the width

    ∵ The perimeter of a rectangle = 2 (l + w)

    ∴ The perimeter of the base = 2 (6 + 5) = 2 (11)

    ∴ The perimeter of the base = 22 units

    Use the formula of the lateral area to find it

    ∵ LA = p * h

    ∴ LA = 22 * 4 = 88 units²

    The lateral area is 88 units²

    ∵ The area of a rectangle = l * w

    ∴ The area of one base of the rectangular prism = 6 * 5

    ∴ The area of one base = 30 units²

    - Multiply it by 2 to find the area of the two bases

    ∴ The area of two bases = 30 * 2 = 60 units²

    The area of the two bases together is 60 units²

    Use the formula of the total surface area to find it

    ∵ SA = LA + area of the two bases

    ∴ SA = 88 + 60 = 148 units²

    The total surface area is 148 units²
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