Calculate Parallelogram Area Using 4:7 Ratio: Height = 8 Units

Question

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

Calculate the area of the parallelogram ABCD.

00:00 Find the parallelogram area

00:06 Height to side ratio according to given data

00:14 Multiply by DC to eliminate the fraction

00:21 Multiply by reciprocal to eliminate the fraction

00:35 Set AE value according to given data

00:48 This is DC's size

00:51 Now we'll use the formula to calculate parallelogram area

00:54 Side(DC) multiplied by height(AE)

00:58 Insert appropriate values and solve to find the area

01:02 And this is the solution to the problem

To find the area of the parallelogram ABCD, follow these steps:

Step 1: Assume $AE = 4x$ and $DC = 7x$ . The ratio between AE and DC is given as 4:7.
Step 2: Given $AE = 8$ cm, we can write: $4x = 8$ . Solve for x: $x = 2$ cm.
Step 3: Substitute $x = 2$ into $DC = 7x$ to find DC: $\text{DC} = 7 \times 2 = 14$ cm.
Step 4: The area of the parallelogram is given by base $\times$ height. Here, base $DC = 14$ cm and height $AE = 8$ cm, so the area is: $\text{Area} = 14 \times 8 = 112 \text{ cm}^2.$

Thus, the area of the parallelogram ABCD is $112$ cm².

$112$ cm².