Use trigonometric ratios to find the dimensions you need to calculate the trapezoid's perimeter and area.
Area= 100.5 yds^2
Perimeter= 43.35 yds
Practice makes perfect
We are supposed to find the area and perimeter of the trapezoid.
Area
To find the area, we have to know the length of the trapezoid's parallel sides and its height. If we mark the height in our diagram, we get a right triangle. In this triangle, we know the hypotenuse and we want to find the opposite leg of the reference angle.
Next, we need to find the measure of the second parallel side. For this purpose, we will divide it into three different segments. In two segments, the length is unknown. To determine these lengths, we will write trigonometric equations.
By solving for a and b we can find the length of the second parallel side by adding their lengths with the middle segment.
With this, we can determine the length of the second parallel side.
3.38+11+2.36 = 16.73 yds
Now we have all the dimensions we need to calculate the trapezoid's area.
Perimeter
To calculate the perimeter, we need to find the length of the remaining side which we will label c. To do that, we can use the sine ratio.
By solving for c we can find the length of the remaining side.
