Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

What might be the values of H, A and B in this trapezium, when the area is 432 cm2? ?

Can you explain your answer so I can understand, please :)

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  • 1 month ago

    Here's my guess from the dimensions of the picture:

    h = 16 cm

    a = 18 cm

    b = 36 cm

    But it could be almost anything. The key is that the height times the *average* of the bases must be 432.

    Double-checking my set of numbers:

    16 * (18 + 36)/2

    16 * 27

    = 432 cm²

    Just for the sake of showing the answer can't be unique, here's another set of values:

    h = 12 cm

    a = 30 cm

    b = 42 cm

    12 * (30 + 42)/2

    12 * 36

    = 432 cm²

    And one more:

    h = 18 cm

    a = 16 cm

    b = 32 cm

    18 * (16 + 32)/2

    18 * 24

    = 432 cm²

  • 1 month ago

    There are many answers, but they are probably wanting you to factor out an expression to come up with integer possible outcomes.

    Starting with the equation for the area of a trapezoid:

    A = (a + b)h / 2

    We know the area is 432 cm², so:

    432 = (a + b)h / 2

    Multiply both sides by 2:

    864 = (a + b)h

    Now let's get a prime factorization of 864 to come up with two values that we can use to multiply to get that number:

    864 = 2⁵ * 3³

    So we can just use those values:

    864 = 32 * 27

    So if we say h = 27, then we need (a + b) to be 32.  Making any two values that total 32 will work.  15 + 17 = 32, so:

    a = 15

    b = 17

    h = 27

    There are many others ways to split this up.  This is just one.

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