Calculate Parallelogram Area: 22cm Perimeter with 2cm Height

ABCD is a parallelogram whose perimeter is equal to 22 cm.

Side AB is smaller by 5 than side AD

The height of the parallelogram for the side AD is 2 cm

What is the area of the parallelogram?

Video Solution

Solution Steps

00:13 Let's find the area of the parallelogram.

00:17 First, let's draw the height based on the information given.

00:21 Remember, the perimeter is the sum of all sides.

00:28 In a parallelogram, opposite sides are equal.

00:35 Look at side AD compared to side AB, as described in the data.

00:41 Let's plug in the values into the perimeter formula and solve for side AB.

01:01 Great! We found AB. Now, use it to determine the other sides.

01:13 Next, let's find the area. Multiply height 2 by side length 8.

01:21 And there you have it, the solution!

Step-by-Step Solution

To solve this problem, we will follow these steps:

Let's begin:

Step 1: Calculate side lengths

Given that the perimeter is 22 cm, we have:

\begin{equation} 2(AB + AD) = 22 \end{equation}

The equation simplifies to:

\begin{equation} AB + AD = 11 \end{equation}

We are also given:

\begin{equation} AB = AD - 5 \end{equation}

Substitute this in the first equation:

\begin{equation} (AD - 5) + AD = 11 \end{equation}

\begin{equation} 2AD - 5 = 11 \end{equation}

\begin{equation} 2AD = 16 \end{equation}

\begin{equation} AD = 8 \end{equation}

Now, substitute $AD = 8$ back into the expression for $AB$ :

\begin{equation} AB = 8 - 5 = 3 \end{equation}

Step 2: Calculate the area

With $AD = 8$ cm as the base (since the problem specifies height to $AD$ ) and the given height of 2 cm, the area is calculated as:

\begin{equation} A = \text{base} \times \text{height} = 8 \times 2 = 16 \, \text{cm}^2 \end{equation}

Therefore, the area of the parallelogram is 16 cm².