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Answer 1 · 2018-02-23T11:13:07

#\text{Area}=350\sqrt{2}#

#\text{Length of non-parallel side}=15#

Perimeter is defined as the sum of all the sides (boundaries) of a geometric figure.

Since a trapezoid has four sides and we are given with two of the sides, it is clear that the other two non-parallel sides are equal in measure.

Let's say #x# represents the length of each non-parallel side.

So, we have:

#\text{Perimeter}=2x+40+30#

#\text{100}=2x+40+30#

Solve for #x# to get:

#x=15#

# #
# #

Now draw a right triangle to solve for the height. The dimensions of the triangle would be:

#\text{Hypotenuse=15}# #" "# #\text{Adjacent}={40-30}/2=5#

#\text{Height}=h=\sqrt{15^2-5^2}#

#h=10\sqrt{2}#

# #
# #
Find the area of the trapezoid by applying the formula:

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# #
# #
#\text{Area} = \frac{40+30}{2}\cdot 10\sqrt{2}#

Simplify:

#=350\sqrt{2}#

# #
# #

That's it!