Question #0a6f5

1 Answer
Feb 23, 2018

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

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

Explanation:

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:

enter image source here



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

Simplify:

=350\sqrt{2}


That's it!