Perimeter, Circumference, and Area
Introduction
Understanding basic geometric calculations is essential for building a strong math foundation. Here’s a quick guide on finding the perimeter, circumference, and area of various shapes:
Core Skills
1. Perimeter of a Shape
The perimeter of a shape is the total distance around its outer edge, found by summing the lengths of all its sides.
Example: The perimeter of a square with side length 4 is calculated as:
\[ 4 + 4 + 4 + 4 = 16 \]
2. Circumference of a Circle
The circumference, or total distance around a circle, is calculated using the following formula, where r
is the radius:
\[ C = 2 \times π \times r \]
If given the diameter d, you can find the radius by dividing it by 2:
radius \[ r = { d \over 2} \]
Example: Find the circumference of a circle with a diameter of 4:
Radius \[ r = { 4 \over 2} = 2 \]
Circumference \[ C = { 2 \times \pi \times 2} \]
3. Area of a Rectangle
The area of a rectangle is found by multiplying its length by its width:
\[ Area = length \times width \]
Example: For a rectangle with side lengths 4 and 5:
\[ Area = 4 \times 5 = 20 units^2 \]
4. Area of a Circle
The area of a circle is calculated as:
\[ Area = \pi \times r^2 \]
Example: Find the area of a circle with a radius of 3 cm:
\[ Area = \pi \times 3^2 =\pi \times 9 ≈ 28.27cm^2 \]
Conclusion
Grasping these basic formulas will make calculating perimeters, circumferences, and areas much easier. Happy calculating!
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