Perimeter:
The perimeter is the total length of the boundary or outline of a two-dimensional shape. It tells you how long it would take to walk around the shape if you followed its edges.
Here are some common formulas for calculating the perimeter of basic shapes:
- Rectangle:
- A rectangle has two pairs of equal sides: length and width.
- Formula: P=2×(Length+Width)
- Square:
- A square has four equal sides.
- Formula: P=4×Side
- Triangle:
- A triangle has three sides.
- Formula: P=Side1+Side2+Side3
- Circle:
- The perimeter of a circle is called the circumference.
Formula: C=2×π×Radius (Where pi= 3.14159
Area:
The area is the amount of space enclosed by a shape. It tells you how much surface is covered by the shape, and it is always measured in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), etc.
Here are formulas for calculating the area of basic shapes:
- Rectangle:
- The area of a rectangle is found by multiplying the length by the width.
- Formula: A=Length×Width
- Square:
- The area of a square is calculated by squaring the length of one of its sides.
- Formula: A=Side^2
- Triangle:
- The area of a triangle is found using the base and the height. The height is the perpendicular distance from the base to the top vertex.
- Formula: A=1/2×Base×Height
- Circle:
- The area of a circle is calculated by squaring the radius and multiplying it by π\pi.
- Formula: A=π×(Radius)^2
Key Differences Between Perimeter and Area:
- Perimeter measures the distance around the shape. It is a linear measurement (one-dimensional).
- Area measures the total space within the shape. It is a surface measurement (two-dimensional).
Summary:
- Perimeter: Total distance around the boundary of a shape.
- Measured in linear units.
- For a rectangle: P=2×(Length+Width)
- For a circle: P=2×π×Radius
- Area: Total space enclosed by the shape.
- Measured in square units.
- For a rectangle: A=Length×Width
- For a circle: A=π×(Radius)^2
Both concepts are fundamental in geometry and are used in a wide range of applications, from architecture and engineering to everyday tasks like determining the amount of material needed to cover a surface or fencing required for a garden.
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