Area of 2D Shapes Formulas
The area of a two-dimensional (2D) shape is the amount of space it covers. It is measured in square units, such as square centimeters (cm²) or square inches (in²). Here are the formulas for calculating the area of some common 2D shapes:
1. Square
A square is a quadrilateral with four equal sides and four right angles.
Formula:
Area = side * side = s²
Where:
- s = length of a side
2. Rectangle
A rectangle is a quadrilateral with four right angles and opposite sides that are equal in length.
Formula:
Area = length * width = l * w
Where:
- l = length
- w = width
3. Triangle
A triangle is a polygon with three sides and three angles.
Formula:
Area = (1/2) * base * height = (1/2) * b * h
Where:
- b = length of the base
- h = height (perpendicular distance from the base to the opposite vertex)
4. Circle
A circle is a closed curve where all points are equidistant from a central point.
Formula:
Area = π * radius² = πr²
Where:
- π = approximately 3.14159
- r = radius (distance from the center to any point on the circle)
5. Parallelogram
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.
Formula:
Area = base * height = b * h
Where:
- b = length of the base
- h = height (perpendicular distance between the base and the opposite side)
6. Trapezoid
A trapezoid is a quadrilateral with one pair of parallel sides.
Formula:
Area = (1/2) * height * (base1 + base2) = (1/2) * h * (b1 + b2)
Where:
- h = height (perpendicular distance between the two parallel sides)
- b1 = length of one base
- b2 = length of the other base
Understanding these formulas will allow you to calculate the area of various 2D shapes. Remember to use the correct units for your measurements and express the final answer in square units.
