Answer: 20
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Explanation:
It might help to rotate the figure so the parallel sides are horizontal. This is optional.
The parallel bases are [tex]b_1 = 6[/tex] and [tex]b_2 = 4[/tex] in either order.
The height is h = 4 which is always perpendicular to both bases.
Plug these values into the trapezoid area formula.
[tex]A = \frac{h(b_1 + b_2)}{2}\\\\A = \frac{4(6+4)}{2}\\\\A = \frac{4(10)}{2}\\\\A = \frac{40}{2}\\\\A = 20\\\\[/tex]
The area of the trapezoid is 20 square units.
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Another pathway is to break the trapezoid into a rectangle up top and a triangle down below.
The rectangle is 4 by 4 with area 4*4 = 16
The triangle has a base of 6-4 = 2 and height of 4, so its area is base*height/2 = 2*4/2 = 8/2 = 4
Overall the total area is rectangle+triangle = 16+4 = 20 square units.
