(3) Area of Polygons Part 1

Area Overview

• Area is a measure of the amount of space within a shape.

• Basic shapes often reviewed for area calculations include squares, rectangles, parallelograms, triangles, trapezoids, and kites.

Square

• Definition: A square is a shape with all four sides of equal length and all angles equal to 90 degrees.

• Area Formula: The area of a square is given by the formula:Area = s²where s is the length of a side.

  • Example: For a square with a side length of 4 units, the area is:Area = 4² = 16 square units.

Rectangle

• Definition: A rectangle is similar to a square, but the lengths of adjacent sides can differ.

• Area Formula: The area of a rectangle is calculated as:Area = base × height.

  • Here, base and height are the lengths of the rectangle's sides.

  • Height is defined as the perpendicular distance from the base to the opposite side, also known as the altitude.

Parallelogram

• Definition: A parallelogram has opposite sides that are parallel and equal in length.

• Area Formula: The area of a parallelogram is given by the same formula as a rectangle:Area = base × height.

  • This is derived by considering the height and the base, making it easy to visualize by transforming it into a rectangle.

Triangle

• Definition: A triangle is a three-sided shape, which can be right-angled or oblique.

• Area Formula: The area of a triangle can be thought of as half of a rectangle: Area = (base × height) / 2.

  • To visualize this, duplicating and positioning a triangle can show how it can form a rectangle when calculated accordingly.

Trapezoid

• Definition: A trapezoid is a quadrilateral with at least one pair of parallel sides, known as the bases.

• Area Formula: The area of a trapezoid is calculated using the bases and height: Area = (base1 + base2) × height / 2.

Kite

• Definition: A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal.

• Area Formula: The area of a kite can be calculated using its diagonals:Area = (D1 × D2) / 2where D1 and D2 are the lengths of the diagonals.

  • The diagonals intersect at right angles, and only half of the diagonals are considered in area calculations.

Summary of Area Calculation Techniques

• Each shape has a unique formula based on its properties, but often these can be derived from more familiar shapes (e.g., triangles as halves of rectangles).

• Understanding the concepts of base and height are crucial for effective area calculations.