Geometry

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1. What is the base and the height of the rectangle if the area is 216 and the perimeter is 66?
2.The perimeter of an isosceles trapezoid is 40 ft. Thr bases of the trapezoid are 11ft and 19 ft. Find the area of the trapezoid.

  • Geometry -

    1. base -- b
    height ==h

    bh = 216
    2b + 2h = 66
    b+h = 33
    h = 33-b

    then b(33-b) = 216
    b^2 - 33b + 216=0
    (b-24)(b-9) = 0
    b = 24 or b=9

    if b=24, h = 33-24 = 9
    if b = 9 , h = 33-9 = 24

    the rectangle is 24 by 9, (you can call either one the base, then the other is the height)

    2. Make a sketch, label each of the equal sides x
    construct right-angled triangles at each end
    So you have a rectangle + 2 equal right-angled triangles
    in each of those triangles, the hypotenuse is x
    the base is 4
    Find the height using Pythagoras,
    the rest is easy.

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