![]() We could at this point substitute b 2/b 1Įxpression for the area of the triangle, but let's keep it in terms of The area of the triangle is therefore T = 1/2 b 1 H = 1/2 b 1 h /(1 - r). The scaling factor of r again applies, and so we get H = h(1 Geometric series to find the altitude H of the triangle in terms of h. Next, let's find the area of the triangle in terms of b 1 and h, using a This is just an infinite geometric series in r 2, Since the scaling factor is r n andĪrea is proportional to the square of the scaling factor, the area of The next thing we want to do is to find the area of the nth trapezoid b 3 = r 2 b 1Īnd for the nth trapezoid the scaling factor will be r n. The scaling factorĪpplies the scaling factor r to BEFC and so has a scaling factor of r 2. By taking the height of BEFC to be rh, it will be similar to ABCD. ![]() Since b 2 is the bottom base for BEFC, the scaling factor r = b 2/b 1. ![]() We want trapezoid BEFC to be similar to ABCD. The trapezoid whose area A we want to find is ABCD given the lengths ofĪBCD has b 2 for its bottom base instead of b 1. The area of the triangle allows us to solve for the area of the We will then find another geometric series to find the area We will use the geometric series to express theĪrea T of the triangle in terms of the base trapezoid. Triangle by layering copies of the trapezoid as show in the The strategy for finding the area of the trapezoid is to build a
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