2D Area Notes

Area Formulas

Rectangle

  • Area Formula: Area = length × width

    • A rectangle is defined by its two dimensions: length and width. The area represents the total space enclosed within the rectangle's four sides.

    • Example: For a rectangle with a length of 5 units and a width of 3 units, the area would be 5 × 3 = 15 square units.

Right Triangle

  • Area Formula: Area = 1/2 × base × height

    • A right triangle is characterized by one right angle (90 degrees). The base and height are perpendicular to each other, forming the right angle.

    • Example: For a right triangle with a base of 4 units and a height of 3 units, the area would be 1/2 × 4 × 3 = 6 square units.

Acute Triangle

  • Area Formula: Area = 1/2 × base × height (general formula for all triangles)

    • An acute triangle has all angles less than 90 degrees. The area can be calculated similarly by identifying any side as the base and determining the height from that base perpendicular to it.

    • Example: For an acute triangle with a base of 6 units and a height of 4 units, the area would be 1/2 × 6 × 4 = 12 square units.

Parallelogram

  • Area Formula: Area = base × height

    • A parallelogram consists of opposite sides that are equal and parallel. The height is the perpendicular distance from the base to the opposite side.

    • Example: For a parallelogram with a base of 10 units and a height of 5 units, the area would be 10 × 5 = 50 square units.

Trapezoid

  • Area Formula: Area = 1/2 × (base1 + base2) × height

    • A trapezoid has at least one pair of parallel sides (base1 and base2). The height is the perpendicular distance between the two bases. The formula considers both bases in the calculation of the area.

    • Example: For a trapezoid with bases of 8 units and 5 units and a height of 4 units, the area would be 1/2 × (8 + 5) × 4 = 26 square units.

Regular Pentagon

  • Finding Area: Area = (1/4) × √(5(5 + 2√5)) × side²

    • A regular pentagon has five equal sides and angles. The formula incorporates the side length to derive the total area.

    • Example: For a regular pentagon with a side length of 4 units, the area would be (1/4) × √(5(5 + 2√5)) × 4² ≈ 11.69 square units.

Regular Hexagon

  • Finding Area: Area = (3√3/2) × side²

    • A regular hexagon features six equal sides and can be divided into six equilateral triangles. The formula uses the side length to calculate the area by combining the area of these triangles.

    • Example: For a regular hexagon with a side length of 3 units, the area would be (3√3/2) × 3² ≈ 11.69 square units.