A prism has a height of 11.2 cm in an equilateral triangle for a base for each base is 8 cm find the volume round answer to the nearest hund

Question

A prism has a height of 11.2 cm in an equilateral triangle for a base for each base is 8 cm find the volume round answer to the nearest hundred

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Maya 3 weeks 2021-09-21T14:27:33+00:00 1 Answer 0

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    2021-09-21T14:28:54+00:00

    Answer:

    310.35cm^3

    Step-by-step explanation:

    Volume of a Prism=Base Area X Height

    The base is an equilateral triangle of side 8cm.

    We can find the area of the triangle using Herons Formula.

    Given a triangle with sides a,b and c

    Area\sqrt{s(s-a)(s-b)(s-c)}

    Where:

    Semiperimeter, s=\frac{a+b+c}{2}

    The sides are of length 8cm, 8cm and 8cm.

    Therefore:

    s=\frac{8+8+8}{2}=12cm

    Area=\sqrt{12(12-8)(12-8)(12-8)}=27.71cm^2

    Since Base Area =27.71cm^2

    Volume=27.71*11.2

    =310.35cm^3

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