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?
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.