Calculate Isosceles Trapezoid Area: Given h=5cm, P=34cm, and BC=7cm

Question

Shown below is the isosceles trapezoid ABCD.

Given in cm:
BC = 7

Height of the trapezoid (h) = 5

Perimeter of the trapezoid (P) = 34

Calculate the area of the trapezoid.

00:00 Calculate the area of the trapezoid

00:03 Let's use the formula for calculating the area of a trapezoid

00:07 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2

00:12 The perimeter of the trapezoid equals the sum of its sides

00:22 According to the given data, it's an isosceles trapezoid

00:27 Let's substitute appropriate values to find the sum of the bases

00:41 Let's isolate the sum of bases(AB+DC)

00:45 This is the size of the sum of bases

00:49 Now let's substitute appropriate values in the area formula and calculate the area

00:57 And this is the solution to the problem

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:

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