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