A plane quadrilateral is a polygon with four sides and four vertices that lies entirely within a single plane. As shown in the figure, it has exactly four vertices labeled A, B, C, and D, connected by four sides. All these elements lie on the same flat surface, which is why we call it a plane quadrilateral.
There are several common types of quadrilaterals. A square has all sides equal and all angles 90 degrees. A rectangle has all angles 90 degrees with opposite sides equal. A rhombus has all sides equal. A parallelogram has opposite sides parallel and equal. And a trapezoid has one pair of opposite sides parallel. Each type has its own unique properties and applications in geometry.
Quadrilaterals have several important properties. First, the sum of interior angles in any quadrilateral is always 360 degrees. Every quadrilateral has exactly two diagonals that connect opposite vertices. In special cases like parallelograms, these diagonals bisect each other. The area of a quadrilateral can be calculated using the formula one-half times the product of the diagonals, when they're perpendicular. And the perimeter is simply the sum of all four sides.
Let's explore how to calculate the area of different quadrilaterals. For a square, the area is simply the square of its side length. For a rectangle, multiply length by width. For a parallelogram, multiply the base by the height, where the height is the perpendicular distance between parallel sides. For a trapezoid, the area is half the product of the height and the sum of the parallel sides. For any quadrilateral, we can use the formula involving the product of the diagonals and the sine of the angle between them. Let's demonstrate the parallelogram formula with our example, where we multiply the base by the height to get the area.
To summarize what we've learned about plane quadrilaterals: They are four-sided polygons with four vertices that lie in a single plane. Common types include squares, rectangles, rhombuses, parallelograms, and trapezoids, each with unique properties. All quadrilaterals share certain characteristics, such as having interior angles that sum to 360 degrees. The area calculation method varies depending on the specific type of quadrilateral. These shapes are fundamental in geometry and have numerous applications in fields like architecture, engineering, and design.