The number sentence to be used to find the perimeter of a composite figure is a straightforward equation that sums all its outer side lengths.
The Perimeter Number Sentence
To determine the perimeter of any composite figure, you add the lengths of all its exterior sides. The general number sentence (formula) that represents this concept is:
P = s₁ + s₂ + s₃ + ... + sₙ
Where:
- P represents the Perimeter of the composite figure.
- s₁, s₂, s₃, ..., sₙ represent the individual lengths of each exterior side of the figure. The "n" signifies that you continue adding until all outer sides have been included.
Understanding the Components
Finding the perimeter involves measuring the total distance around the outside edge of a shape. For a composite figure—which is a shape made up of two or more basic geometric shapes—this means tracing its entire boundary and summing the lengths of each segment.
| Term | Description |
|---|---|
| Perimeter (P) | The total distance around the outer boundary of the composite figure. |
| Side Length (s) | The measured length of an individual segment forming the outer edge of the figure. |
| Summation | The act of adding together all the individual side lengths. |
How to Apply the Number Sentence
- Identify All Exterior Sides: Carefully examine the composite figure to distinguish all the side lengths that form its outer boundary. Interior lines (where two basic shapes might join) are not part of the perimeter.
- Measure or Use Given Lengths: For each exterior side, use its given measurement or calculate it if it's missing (e.g., by subtracting known lengths from total lengths).
- Add Them Up: Substitute the numerical values of each identified side length into the number sentence and perform the addition.
Example:
Imagine a composite figure made of a rectangle and a triangle, where the shared side is internal. You would only consider the outer edges of both shapes. If the outer sides measure 5 cm, 7 cm, 4 cm, 3 cm, and 6 cm, the number sentence would be:
P = 5 cm + 7 cm + 4 cm + 3 cm + 6 cm
P = 25 cm
This fundamental number sentence provides the method for calculating the perimeter for any composite figure by simply summing all of its outer side lengths.
