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Math Help - Area of a region

  1. #1
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    Area of a region

    The diagram shows a logo ABCD in the shape of a trapezium. AB=13x cm, CD=12x cm, AD=2y cm and Angle BCD = 90^o. The shaded region PQDR is a parallelogram such that RD=\frac{1}{3}AD.

    Before reaching the part i have problems with,

    BC=2y+5x and area of ABCD=\frac{1}{2}(4y+5x)(6x)

    The question is Find the area of PQDR
    Last edited by Punch; October 9th 2010 at 06:33 PM.
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  2. #2
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    Quote Originally Posted by Punch View Post
    [FONT=Arial]The diagram shows a logo ABCD in the shape of a trapezium. AB=13x cm, CD=12x cm, AD=2y cm and Angle BCD = 90^o. The shaded region PQDR is a parallelogram such that AD=\frac{1}{3}AD.<=== typo? RD = ...
    Before reaching the part i have problems with,

    BC=2y+5x and area of ABCD=\frac{1}{2}(4y+5x)(6x)

    The question is Find the area of PQDR
    1. The right triangle at the left with the hypotenuse \overline{AB} has one leg with the length 12x. Use Pythagorean theorem to determine the length of the missing leg (<--- no pun intended!)

    2. The area of a trapezium is calculated by:

    a = \dfrac{\overline{AD} + \overline{BC}}2 \cdot \overline{DC}

    with \overline{AD} = 2y

    \overline{BC} = 5x + 2y

    \overline{DC} = 12x
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  3. #3
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    Indeed that was a typo. However, the question hasn't been answered!

    The question is Find the area of PQDR
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  4. #4
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    Quote Originally Posted by Punch View Post
    Indeed that was a typo. However, the question hasn't been answered!

    The question is Find the area of PQDR
    1. PQDR is a parallelogram.

    2. To determine the area of a parallelogram you need the length of the base and the length of the height. All values are known to you.

    3. So, where are your difficulties?
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  5. #5
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    Quote Originally Posted by earboth View Post
    1. PQDR is a parallelogram.

    2. To determine the area of a parallelogram you need the length of the base and the length of the height. All values are known to you.

    3. So, where are your difficulties?

    I dont have the value of side PR or QD, note that it is not parallel to side AB
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  6. #6
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    Quote Originally Posted by Punch View Post
    I dont have the value of side PR or QD, note that it is not parallel to side AB
    1. The area of a parallelogram is calculated by:

    area = base \cdot height

    2. Take \overline{PQ} = \dfrac23 y as the base then the corresponding height is \overline{DC} = 12x

    3. Thus the area of the parallelogram is:

    a = \dfrac23 y \cdot 12x = 8xy
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  7. #7
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    Quote Originally Posted by earboth View Post
    1. The area of a parallelogram is calculated by:

    area = base \cdot height

    2. Take \overline{PQ} = \dfrac23 y as the base then the corresponding height is \overline{DC} = 12x

    3. Thus the area of the parallelogram is:

    a = \dfrac23 y \cdot 12x = 8xy
    Oh my... Sorry!! I was mistaken that the height was referring to RQ

    Thanks
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