Area of ​​Special Quadrilaterals

$A = s^{2} = 5^{2} = 25 \text{cm}^{2}$

$A = s^{2} = 9^{2} = 81 \text{ m}^{2}$

$A = b \times h = 6 \times 3 = 18 \text{ in}^{2}$

$A = b \times h = 4 \times 6 = 24 \text{ cm}^{2}$

$A = l \times w = 10 \times 14 = 140 \text{ cm}^{2}$

$A = l \times w = 8 \times 12 = 96 \text{ in}^{2}$

$A = \frac{1}{2}(a + b) \times h = \frac{1}{2}(10 + 6) \times 4 = 32 \text{ ft}^{2}$

$A = \frac{1}{2}(a + b) \times h = \frac{1}{2}(5 + 3) \times 2 = 8 \text{ m}^{2}$

A special quadrilateral is a four-sided polygon with distinct properties that differentiate it from other quadrilaterals, such as squares, rectangles, parallelograms and trapezia.

The area of a square is calculated by squaring the length of one of its sides, expressed as $ A = s^{2} $.

The area of a rectangle is calculated by multiplying the length by the width, expressed as $ A = l \times w $.

For parallelograms, the area is calculated using the base and the perpendicular height, not the slant height, as $ A = b \times h $, where $ b $ is the base and $ h $ is the height.

The area of a trapezoid is found by averaging the lengths of the two parallel sides and multiplying by the perpendicular height, expressed as $ A = \frac{1}{2}(a+b) \times h $.

Using square units is crucial as area represents a two-dimensional space, and square units quantify the amount of space inside the boundary of a shape.

Knowing how to calculate the area of special quadrilaterals can assist in various real-world tasks, such as material estimation for construction, interior design, landscaping, and more.

Understanding the geometric properties of each quadrilateral helps in remembering their specific area formulas—like knowing that a square's sides are equal, or a trapezium has one set of parallel sides.

Yes, a rectangle is a special type of parallelogram with right angles. Though we often label a rectangle using length and width and a parallelogram using base and height, the area for each is found by multiplying the two perpendicular sides.