Area of a Trapezoid: Finding Area based off Perimeter and Vice Versa

We begin by inserting any given data into the formula to find the area of a trapezoid:

$S=\frac{(AB+CD)\times h}{2}$

We identify AD as the height of the trapezoid

$35=\frac{(6+8)\times AD}{2}$

$35=\frac{14}{2}AD$

$35=7AD$

We then divide the two sections by 7:

$5=AD$

Finally we calculate the perimeter by adding together all the sides as follows:

$5+6+8+5.5=11+8+5.5=19+5.5=24.5$

Since ABCD is a trapezoid, one can determine that:

$AD=BC=7$

Thus the formula to find the area will be

$$$S_{ABCD}=\frac{(AB+DC)\times h}{2}$

Since we are given the perimeter of the trapezoid, we can find$AB+DC$

$P_{ABCD}=7+AB+7+DC$

$34=14+AB+DC$

$34-14=AB+DC$

$20=AB+DC$

Now we will place the data we obtained into the formula in order to calculate the area of the trapezoid:

$S=\frac{20\times5}{2}=\frac{100}{2}=50$