Finding the area of a plane figure is a fundamental concept in geometry. The area is the amount of space inside the boundary of a two-dimensional shape, and different shapes have different methods to calculate their area.
Common Plane Figures and Their Area Formulas
1. Rectangle
A rectangle has opposite sides that are equal and parallel. To find the area of a rectangle, you multiply its length by its width.
$A = l times w$
For example, if a rectangle has a length of 5 units and a width of 3 units, its area would be $5 times 3 = 15$ square units.
2. Square
A square is a special type of rectangle where all sides are equal. The area of a square is found by squaring the length of one of its sides.
$A = s^2$
If each side of the square is 4 units, the area would be $4^2 = 16$ square units.
3. Triangle
The area of a triangle is calculated by taking half of the product of its base and height.
$A = frac{1}{2} times b times h$
For instance, if the base of a triangle is 6 units and its height is 4 units, the area is $frac{1}{2} times 6 times 4 = 12$ square units.
4. Circle
To find the area of a circle, you use the formula involving the radius (the distance from the center to any point on the circle).
$A = pi r^2$
If the radius of the circle is 3 units, the area would be $pi times 3^2 = 9pi$ square units.
5. Parallelogram
A parallelogram has opposite sides that are equal and parallel. Its area is found by multiplying the base by the height.
$A = b times h$
For example, if the base is 7 units and the height is 5 units, the area is $7 times 5 = 35$ square units.
6. Trapezoid
A trapezoid has one pair of parallel sides. To find its area, you take the average of the lengths of the parallel sides (bases) and multiply by the height.
$A = frac{1}{2} times (b_1 + b_2) times h$
If the lengths of the bases are 8 units and 5 units, and the height is 4 units, the area is $frac{1}{2} times (8 + 5) times 4 = 26$ square units.
Conclusion
Understanding the formulas for finding the area of various plane figures is essential in geometry. Whether you’re dealing with rectangles, squares, triangles, circles, parallelograms, or trapezoids, knowing these formulas allows you to calculate the area efficiently and accurately.
3. CK-12 – Area of Plane Figures