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the sides of the trapezoid in the
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diagram are equal to 3 4 4 and 9 find
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its area as usual pause the video before
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watching to try solving it yourself
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we'll go through two methods of solving
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this problem first method let's label
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the vertices and extend one of the
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lateral sides which has the smaller base
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of the trapezoid to form a parallelogram
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it doesn't matter which lateral side we
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choose the solution will be similar in
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either case for instance let's extend
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the lateral side AB and the base b c to
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form a parallelogram to do this draw a
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line through Point C parallel to a b
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until it intersects the base a d at
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Point e the opposite sides of a
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parallelogram are equal so c will be
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equal to a which is 3 and AE will be
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equal to b c which is four then D will
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be equal to a D minus a e resulting in
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five we have now formed an Egyptian
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right triangle CDE e where the sides are
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3 4 and 5 meaning the angle at DC is 90°
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the area of the right triangle dce can
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be found as half the product of its legs
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which gives six square units to find the
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remaining part of the trapezoid that is
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to find the area of the parallelogram a
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b c e draw its diagonal a c the
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triangles AC e and DC e will have the
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same height so the ratio of their areas
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will be equal to the ratio of their
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corresponding bases which is 4 FS
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therefore the area of triangle a will be
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4 fths of the area of triangle
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dce thus the area of trapezoid AB c d
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which is the sum of the areas of the
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parallelogram AB c e and triangle
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dce will be equal to replacing the area
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of the parallelogram with twice the area
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of triangle AC e substituting the
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expression for the area of triangle AC
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through the area of triangle d c e and
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obtaining 13 fths of the area of
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triangle d c e which equals 6 as a
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result we get 78 fths or 15.6 second
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method draw a height c h from the vertex
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C of the right triangle d c e which
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represents the height of the trapezoid a
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b c d we find this height using the
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formula for the area of the right
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triangle d c e on one hand the area of
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triangle d c e is equal to half the
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product of its legs and on the other
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hand the area is equal to half the
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product of height c h and the base d e
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from the last equation we find c h to be
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the area of trapezoid a b c d using the
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standard formula can be found as the
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product of the half sum of the bases and
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the height c h substituting we get the
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same result write the answer the area of
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the trapezoid is 15.6 square units the
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problem is solved if you understood the
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solution like the video leave a comment
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