Trapezoid Perimeter Calculation: Area = 35 cm² with Given Side Lengths

Question

Look at the trapezoid in the figure.

Its area is equal to 35 cm².

Calculate its perimeter.

00:00 Calculate the perimeter of the trapezoid

00:03 We'll use the formula for calculating the area of a trapezoid

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

00:14 Let's substitute appropriate values according to the given data and solve for the height

00:21 In this case, the height is side AD

00:42 Let's isolate AD

00:47 This is the size of AD, now we can calculate the trapezoid's perimeter

00:53 The perimeter of the trapezoid equals the sum of its sides

01:06 Let's substitute the values of the sides and solve for the perimeter

01:19 And this is the solution to the question

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:

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

$24.5$ cm