What is the perimeter of the isosceles trapezoid that has vertices of #A(-3, 5), B(3, 5), C(5, -3),# and #D(-5, -3)#?
1 Answer
Explanation:
I would approach this problem in 3 steps:
1) Determine the length of the flat lines (the ones parallel to the
2) Determine the length of the angled lines through the use of the Pythagorean Theorem, and
3) Find the sum of these values.
Let's start with the basic part: Determining the length of the flat lines.
You know that this trapezoid has 4 sides, and based of the coordinates, you know 2 of the sides are flat, and therefore easy to measure the length of.
In general, flat lines, or lines parallel with the
In your case, there is no change in
These two lines are between points
Both line
For
For
Next, we'll get the length of each of the slanted lines, which should conveniently be the same because this is an isosceles trapezoid.
We can achieve this through the use of the Pythagorean Theorem:
Where:
For sake of ease, we'll use line
To get change in
Plug them in and you get:
We'll use a similar equation for change in
Again, plug and chug to get:
You now have your
Since we have the same line twice, but just reflected, we can use the same length twice.
For our final perimeter, we'll get:
Which simplifies to: