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13 May, 07:15

Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6 in. The height of the prism is 10 in

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  1. 13 May, 07:32
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    The surface area = 211.2 inches²

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - The prism has triangular base

    - The base is equilateral triangle

    - The surface area of any prism = lateral area + 2 base area

    - The lateral area = perimeter of base * its height

    - The perimeter of the equilateral triangle = 3L, where L is the length

    of its side

    ∴ The lateral area = 3L * h = 3Lh

    - Area of the equilateral triangle = 1/2 * L * L * sin (60)

    Area of the equilateral triangle = 1/2 * L * L * √3/2

    Area of the equilateral triangle = √3/4 L²

    ∴ The surface area = 3Lh + 2 (√3/4 L²) = 3Lh + √3/2 L²

    ∵ The side length (L) of the equilateral Δ = 6 inches

    ∵ The height (h) of the prism = 10 inches

    ∴ The surface area = 3 (6) (10) + √3/2 (6²)

    ∴ The surface area = 180 + 18√3 = 211.18

    * The surface area = 211.2 inches²
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