The area of a two-dimensional (2D) shape is the measure of the extent of the surface enclosed by the shape. It quantifies the amount of space inside the boundaries of the shape and is expressed in square units. The formula for calculating the area depends on the type of 2D shape.
Area of a Rectangle:
A rectangle is a quadrilateral with four right angles.
Area=length×width
Example: If a rectangle has a length of 6 units and a width of 4 units, the area is 6×4=24 square units.
Area of a Square:
A square is a special type of rectangle with all sides equal.
Area=\(side×side \) or \(\text{Area} = \text{side}^2\)
Example: For a square with sides of length 6 units, the area is 6 x 6 =36 square units.
Area of a Triangle:
A triangle is a three-sided polygon.
\(\text{Area}\) = \(\frac{1}{2} \times \text{base} \times \text{height}\)
Example: In a triangle with a base of 8 units and a height of 6 units, the area is \(\frac{1}{2} \times 8 \times 6 = 24 \, \text{square units}\)
Area of a Circle:
A circle is a set of all points equidistant from a central point.
\(\text{Area}\) = \(\pi \times \text{radius}^2\)
Example: If a circle has a radius of 3 units, the area is \(\pi \times 3^2 \approx 28.27 \, \text{square units}\)
Area of a Parallelogram:
A parallelogram is a four-sided figure with opposite sides parallel.
\(\text{Area}\) = \(\text{base} \times \text{height}\)
Example: For a parallelogram with a base of 7 units and a height of 5 units, the area is 7×5=35 square units.
Area of a Trapezoid:
A trapezoid is a quadrilateral with one pair of parallel sides.
\(\text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}\)
Example: In a trapezoid with parallel sides of lengths 6 units and 8 units, and a height of 4 units,
the area is \( \frac{1}{2} \times (6 + 8) \times 4 = 28 \, \text{square units}\)