Maths mensuration

ABCD is a parallelogram with sides AB=12cm,BC=10cm and diagonal Ac=16cm.find the area of parallelogram. Also find the distance between its shorter side.

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  1. several ways of doing this:

    1. use Heron's formula
    split the parallelogram into 2 congruent triangles, then apply using
    http://www.mathwarehouse.com/geometry/triangles/area/herons-formula-triangle-area.php

    2. Use the cosine law to find the obtuse angle between the two sides 12 and 10
    16^2 = 12^2 + 10^2 - 2(12)(10)cosØ

    once you have angle Ø
    area of ||gram = (12)(10)sinØ

    Once you have the area,
    use 10 as the base, and let the distance between the two short sides by h, your required altitude.

    area = base x height
    area = 10h
    solve for h, since you have the area from above

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