Mathematics

Question

Marco and Elaine are building a stand like the one shown to display trophies.
Marco and Elaine are building a stand like the one shown to display trophies.

2 Answer

  • The surface area is basically the sum of all the exposed area of the figure given in the pictures. Since all sides are rectangular, the area can be calculated through the equation,
                                     Area = length x width
    The total surface area of the figure is 58 ft².
  • Answer:

    68 square feet is the total surface area of the stand.

    Step-by-step explanation:

    Since both the parts of the stand are in the shape of prism.

    Therefore surface area of the stand = surface area of horizontal prism + surface area of vertical prism

    Since the formula of surface area of prism = 2(lw + lh + hw)

    where l = length, w = width, h = height

    Now for horizontal prism

    l = 7 ft. , w = 1 ft. , h = 2 ft

    Therefore area of horizontal prism = 2(7×1 + 7×2 + 2×1) = 2×23 = 46 square feet

    Now dimensions of the vertical prism

    l = 3 ft. , w = 2 ft. , h = 1 ft.

    and area = 2(3×2 + 3×1 + 1×2) = 2(11) = 22 square feet.

    Now the area of whole structure will be = 46 + 22 = 68 square feet.

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