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?
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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?
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 back into the expression for :
\begin{equation} AB = 8 - 5 = 3 \end{equation}Step 2: Calculate the area
With cm as the base (since the problem specifies height to ) 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.
16 cm²
A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.
Calculate the area of the parallelogram.
The problem states "the height for side AD is 2 cm." This means the 2 cm height is perpendicular to side AD, not to side AB. Using AB would require a different height measurement.
In parallelogram ABCD, opposite sides are AB and DC, and AD and BC. These pairs are always equal in length, which is why the perimeter formula is .
Start with the simpler relationship first! Since is already solved for AB, substitute this into the perimeter equation .
Yes! Check that AB = 3 cm and AD = 8 cm satisfy both conditions: AB + AD = 11 ✓ and AB is 5 less than AD ✓
For parallelograms, we use base × height where height is the perpendicular distance between parallel sides. This is different from a rectangle's length × width because parallelogram sides are slanted.
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