## Area vs perimeter

### Area and perimeter are two fundamental concepts in geometry that are used to measure and describe geometric figures, such as polygons

Area and perimeter are two fundamental concepts in geometry that are used to measure and describe geometric figures, such as polygons.

1. Area:

The area of a shape refers to the amount of space it occupies within its boundaries. It is essentially the measure of the surface or the “inside” of the shape. The area is always expressed in square units, such as square inches (in²), square centimeters (cm²), or square meters (m²). The formula for calculating the area depends on the shape being considered.

– For square and rectangle: The area is calculated by multiplying the length of one side by the length of an adjacent side. Area = length × width.

– For triangle: The area is calculated by multiplying the base of the triangle by its corresponding height and dividing the result by 2. Area = 1/2 × base × height.

– For circle: The area is calculated by squaring the radius of the circle and multiplying it by π (pi). Area = πr².

– For other irregular shapes, the area can be calculated using calculus or by breaking the shape into smaller, simpler shapes for which the area formulas are known.

2. Perimeter:

Perimeter refers to the total length of the boundary or the “outside” of a shape. It is a measure of the distance around the figure, as if you were walking along its edges. The perimeter is always expressed in linear units, such as inches (in), centimeters (cm), or meters (m). The formula for calculating the perimeter also depends on the shape being considered.

– For square and rectangle: The perimeter is calculated by adding all the lengths of the sides. Perimeter = 2 × (length + width).

– For triangle: The perimeter is calculated by adding the lengths of all three sides. Perimeter = side₁ + side₂ + side₃.

– For circle: The perimeter is called the circumference and is calculated by multiplying the diameter (or twice the radius) by π (pi). Perimeter (circumference) = 2πr or πd.

It is important to note that the area and perimeter measure different aspects of a shape. The area provides information about the size of the shape’s interior or surface, while the perimeter focuses on the length required to enclose the shape.

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