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Math Help - Areas of Triangles

  1. #1
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    Exclamation Areas of Triangles

    A parallelogram has two adjacent sides of length 4 cm and 6 cm respectively. If the included angle measures 52 degrees, find the area of the parallelogram.

    please show all working out.
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  2. #2
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    Quote Originally Posted by Tessarina View Post
    A parallelogram has two adjacent sides of length 4 cm and 6 cm respectively. If the included angle measures 52 degrees, find the area of the parallelogram.

    please show all working out.
    if a and b are the lengths of two adjacent sides of a parallelogram and \theta is the included angle between those two sides, then the area of the parallelogram is given by

     <br />
A = a \cdot b \cdot \sin{\theta}<br />
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  3. #3
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    ../------------|--/
    /Theta------- |/
    6cm
    Area of a parallelogram is given by Base into corresponding altitude..k?
    Now, draw perpendicular to one side.. the other side is found out by:
    sin theta=opposite leg
    --------------
    hypotenuse

    multiplying sin theta by hypotenuse gives us opposite leg.. which in the case of the triangle with one vertex, theta and altitude.. is the altitude..
    so area=a.b.sin theta
    =4*6*sin 52
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  4. #4
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    The area of a triangle is:
    A = \frac{1}{2}a * b * \sin{C}

    From your parallelogram, there are 2 identical triangles if you divide your parallelogram in half.
    From your information, a = 4, b = 6, C = 54^{\circ}.

    There you can work out the area of a triangle, then double it to find the area of your parallelogram.
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