Geometry Formula Cheat Sheet for Shapes, Area and Volume

The geometry formula cheat sheet includes essential area, volume, perimeter, and shape formulas, helping learners understand 2D and 3D figures and solve geometry problems related to measurements and space.

Geometry Formula Cheat Sheet

Topic	Formula	Description
Perimeter of Square	4a	Total boundary of square
Area of Square	a²	Area of square
Perimeter of Rectangle	2(l + w)	Total boundary
Area of Rectangle	l × w	Area of rectangle
Area of Triangle	(1/2) × b × h	Basic triangle area
Heron’s Formula	√[s(s−a)(s−b)(s−c)]	Area using sides
Perimeter of Triangle	a + b + c	Sum of sides
Pythagorean Theorem	a² + b² = c²	Right triangle rule
Area of Parallelogram	b × h	Base times height
Area of Trapezium	(1/2)(a + b)h	Sum of parallel sides
Area of Rhombus	(1/2) d₁d₂	Using diagonals
Circumference of Circle	2πr	Circle boundary
Area of Circle	πr²	Circle area
Arc Length	(θ/360) × 2πr	Length of arc
Sector Area	(θ/360) × πr²	Area of sector
Volume of Cube	a³	Cube volume
Surface Area of Cube	6a²	Total surface
Volume of Cuboid	l × w × h	Rectangular solid
Surface Area of Cuboid	2(lw + lh + wh)	Total surface
Volume of Cylinder	πr²h	Cylinder volume
Surface Area of Cylinder	2πr(h + r)	Total surface
Volume of Cone	(1/3)πr²h	Cone volume
Surface Area of Cone	πr(r + l)	Total surface
Volume of Sphere	(4/3)πr³	Sphere volume
Surface Area of Sphere	4πr²	Total surface
Diagonal of Square	a√2	Square diagonal
Diagonal of Cuboid	√(l² + w² + h²)	Space diagonal
Angle Sum of Triangle	180°	Total angles
Angle Sum of Quadrilateral	360°	Total angles
Interior Angle (Polygon)	((n−2)×180)/n	Each angle
Exterior Angle	360/n	Regular polygon

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Conclusion Geometry is a subdivision of mathematics that concerns itself with form, dimensions, angles, and space. It aids us in comprehending the physical world through studying such objects as lines, triangles, circles, and polygons. In real life, geometry is applied in the fields of architecture, engineering, art and design. It enables us to quantify distances, areas, and volumes of objects. Study of geometry enhances spatial thinking and visualisation, which are relevant in addressing real-life problems. Mathematical concepts such as points, lines, angles, symmetry and transformations are basic concepts in geometry. It also encompasses coordinate geometry, which relates algebra to geometric figures. Geometry can be used to learn about maps, buildings, and even computer graphics. Students can learn to prove statements and solve problems logically by studying the rules and theorems of geometry as well as by step by step. It is also important in applications in physics and engineering. Geometry is not merely learning formulas but also the way forms relate with each other in space. All in all, it is a very necessary component of mathematics, which bridges the gap between theory and practice. To conclude, geometry helps us nearly understand shapes and space. It improves logical reasoning and plays an important role in many real-world applications.