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Calculate the area of each figure below. Show all work.

  1. An enclosed figure:  Down 4, left 9, and up an unknown length, right 5, and a diagonal to the start enclosing the figure. Its length is 4 square root of two..  Three angles are right angles.

    Try breaking up the shape into two rectangles and one triangle as shown below.

    Added to the figure, a horizontal dashed line, coming from the bottom vertex of the slanted side, with a vertical segment, from the horizontal segment, to the top vertex of the slanted side.

    If the bottom length is units, then what must be the total length of the longest dotted line? How does that help you determine the length of the bottom leg of the triangle?

    With the given hypotenuse and side lengths, what could the angle measurements be for the triangle?
    What do the angles say about the missing side length?


  1. A triangle has two equal sides. One of these is labeled 12.  The angle between the two equal sides is 22 degrees.

    Create two right triangles within the isosceles triangle.

    Added to the triangle, a dashed vertical line, from the angle labeled 22 degrees, to the horizontal side.


  1. A right triangle with a hypotenuse of 8 and a leg of 4.

    See hints from parts (a) and (b).