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Thread: Finding Area of Composite Shapes

  1. #1
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    Finding Area of Composite Shapes

    http://www.mhschool.com/math/mathcon...dllsn_onln.pdf
    Go to this link, I need help subdividing question 13's shape. I can find the area on me own but I can't figure out how to subdivide the shape to find the area. Please help.

  2. #2
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    Quote Originally Posted by Butter View Post
    http://www.mhschool.com/math/mathcon...dllsn_onln.pdf
    Go to this link, I need help subdividing question 13's shape. I can find the area on me own but I can't figure out how to subdivide the shape to find the area. Please help.
    Any rectilinear figure (meaning a figure that has a perimeter made up of straight lines) can be "decomposed" into triangles. That means you can draw a set of triangles that fit exactly within the boundaries of the rectilinear figure. Do you understand what "decomposing" a rectilinear figure means now?

    Let's take a really easy example. Draw a rectangle and number the "corners" (more precisely "vertices") of a rectangle as 1, 2, 3, 4 going clockwise. Draw a straight line between corners 1 and 3. You have now decomposed the rectangle into two triangles, one with corners 1, 2, and 3 and the other with corners 3, 4, and 1. You could have done the same thing by drawing a straight line between corners 2 and 4. Does this make sense?

    Some rectilinear figures can be decomposed into rectangles. That is what your are being asked to do here. You are being asked to draw lines between various corners that break the figure up into two or more rectangles. Is it clear now?

    Why do we do this? We have very simple formulas for the area of rectangles and triangles. So if we can break a complicated figure up into triangles or rectangles we can calculate the areas of the simpler pieces and add them up to get the area of the complicated figure.

    Did that help?

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