# The area of an isosceles trapezoid is 246 square meters. If the height and the length of one of its congruent sides measure 6m and 10m, respectively, find the lengths of the two bases.

1
by lalalalang

2015-04-28T20:34:35+08:00

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Since the height, the base, and one of its congruent sides make a triangle, therefore we can use Pythagorean theorem.

10²=a²+6²
100=a²+36
Subtract both sides by 36
64=a²
a=8

Now since the parallel sides of a trapezoid are congruent, we can say that 2 of the sides have the same length

Next I came up with my own formula that:
+2z
or simply
+16

where z is the length we got from the Pythagorean theorem

The formula of the area of the trapezoid is:
A=
A=246 m²
h=6 m
Substitute the values

246 m²=+16 m)
Multiply both sides by 2
492 m²=6 m(+16)
Divide both sides by 6
82 m=+16
Subtract both sides by 16
66 m=
Divide both sides by 2
33 m=

Now we know we have base 1 with 33 m, not lets substitute to find the longer base
=33 m+16 m