Easily calculate areas and perimeters of 2D shapes, and volumes and surface areas of 3D shapes.
A. The area of a circle is πr² (pi × radius²), and the circumference is 2πr (2 × pi × radius). For example, a circle with radius 5cm has an area of about 78.54cm² and circumference of about 31.42cm.
A. Heron's formula is used to find the area of a triangle when you only know the lengths of all three sides but not the height. First calculate s = (a+b+c)/2 (semi-perimeter), then Area = √(s(s-a)(s-b)(s-c)).
A. The area formula for a regular polygon is (n × s² × cot(π/n)) / 4, where n is the number of sides and s is the side length. For example, a regular hexagon with side 6cm has an area of about 93.53cm².
A. With the same base and height, a cone's volume is exactly 1/3 of a cylinder's volume. Cylinder volume = πr²h, Cone volume = (1/3)πr²h.
Calculating areas and volumes of shapes is one of the most fundamental and practical areas of mathematics. The area of a 2D shape represents the size of the two-dimensional space it occupies, while the volume of a 3D shape represents the space it takes up in three dimensions. These calculations are used in architecture, interior design, land surveying, packaging design, and many other real-world applications.
Pi (π) is the ratio of a circle's circumference to its diameter, approximately 3.14159. It is used in calculations for all circle-related shapes (circles, spheres, cylinders, cones), and regular polygons approach a circle as the number of sides increases infinitely. Heron's formula is a powerful tool for finding a triangle's area using only the three side lengths, widely used in surveying and cartography.