Here are some common geometrical shapes along with their formulas for calculating area:

**Rectangle:**

Area = Side × Side (or Side^2)

Example: A square with sides of 4 centimeters each has an area of 16 square centimeters.

**Triangle:**

Area = Length × Width

Example: A room with a length of 5 meters and a width of 3 meters has an area of 15 square meters.

**Square:**

Area = (Base × Height) / 2

Example: A triangle with a base of 6 meters and a height of 8 meters has an area of 24 square meters.

**Circle**:

Area = π × Radius^2

Example: A circle with a radius of 5 meters has an area of approximately 78.54 square meters (using π ≈ 3.14).

**Parallelogram:**

Area = Base × Height

Example: A parallelogram with a base of 7 meters and a height of 9 meters has an area of 63 square meters.

**Trapezoid**:

Area = (Sum of parallel sides / 2) × Height

Example: A trapezoid with parallel sides of 5 meters and 9 meters, and a height of 4 meters, has an area of 28 square meters.

**Rhombus**:

Area = (Diagonal1 × Diagonal2) / 2

Example: A rhombus with diagonals of 6 meters and 8 meters each has an area of 24 square meters.

**Regular Polygon:**

Area = (Perimeter × Apothem) / 2

Example: A regular hexagon with a perimeter of 24 meters and an apothem of 4 meters has an area of 48 square meters.

**Ellipse**:

Area ≈ π × Semi-Major Axis × Semi-Minor Axis

Example: An ellipse with a semi-major axis of 8 meters and a semi-minor axis of 5 meters has an approximate area of 125.66 square meters.

**Sector of a Circle:**

Area = (θ/360) × π × Radius^2

Example: A sector with a central angle of 45 degrees in a circle with a radius of 10 meters has an area of approximately 5.24 square meters.

**Segment of a Circle:**

Area = (Sector Area) – (Triangle Area)

Example: If a segment has a central angle of 60 degrees in a circle with a radius of 7 meters, the segment area is approximately 18.42 square meters.

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