Section Formula: The section formula relates the areas of two related geometric figures based on their corresponding measures. It provides a direct and effi...
Section Formula:
The section formula relates the areas of two related geometric figures based on their corresponding measures. It provides a direct and efficient way to determine the area of a specific section of a larger shape.
Formulas:
Area of the smaller figure = Area of the larger figure × Ratio of the corresponding dimensions
Area of the larger figure = Area of the smaller figure ÷ Ratio of the corresponding dimensions
Example:
Let's say we have a rectangle with length 10 cm and width 5 cm. The area of this rectangle is:
Area = Length × Width = 10 cm × 5 cm = 50 cm²
Now, let's say we cut the rectangle into two equal sections along its width.
The smaller section will have a length of 5 cm and a width of 2.5 cm.
The larger section will have a length of 10 cm and a width of 5 cm.
Using the formula, we can find the areas of these two sections:
Smaller section area = 5 cm × 2.5 cm = 12.5 cm²
Larger section area = 10 cm × 5 cm = 50 cm²
Therefore, the combined area of the two sections is:
Total area = Area of smaller section + Area of larger section = 12.5 cm² + 50 cm² = 62.5 cm²
The section formula allows us to quickly calculate the area of a specific section of a given shape by using the areas of the two corresponding figures