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A large parallelogram is divided into four small parallelograms as shown. The areas of three of the four small parallelograms are labeled in the diagram. What is the area of the remaining small parallelogram?

 Dec 22, 2024
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1. Understand the Problem

 

We have a large parallelogram divided into four smaller parallelograms.

 

The areas of three of the smaller parallelograms are given: 4, 5, and 6.

 

We need to find the area of the remaining small parallelogram.

 

2. Key Concept

 

Parallelograms and Area:

 

In a parallelogram divided by two sets of parallel lines, the product of the areas of opposite parallelograms are equal.

 

3. Solution

 

Let the area of the remaining small parallelogram be 'x'.

 

According to the property mentioned above:

 

Area of parallelogram 1 * Area of parallelogram 3 = Area of parallelogram 2 * Area of parallelogram 4

 

Substitute the given values:

 

4 * 6 = 5 * x

 

Solve for 'x':

 

x = (4 * 6) / 5

 

x = 24 / 5

 

Therefore, the area of the remaining small parallelogram is 24/5.

 Dec 24, 2024

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