What is the difference between area and perimeter?

Area measures the space inside a shape (square units). Perimeter measures the distance around the outside (linear units). A 4×6 rectangle has area 24 cm² and perimeter 20 cm.

How many degrees in a triangle?

The interior angles of any triangle always sum to 180°, regardless of the triangle type.

What is a right angle?

A right angle is exactly 90 degrees, like the corner of a square. A right triangle has one right angle.

Geometry

Shapes, angles, and spatial reasoning

Geometry is the study of shapes, sizes, angles, and spatial relationships. It is everywhere — from architecture to art to engineering. Understanding geometry formulas for area, perimeter, and volume is essential for both academics and real-world applications.

Key Concepts

Area

The space inside a 2D shape. Rectangle: l × w. Triangle: ½ × b × h. Circle: π × r². Each shape has its own formula.

Perimeter

The distance around a shape. Rectangle: 2(l + w). Circle (circumference): 2πr. Triangle: a + b + c.

Volume

The space inside a 3D object. Cube: s³. Cuboid: l × w × h. Cylinder: πr²h. Sphere: (4/3)πr³.

Angles

Angles are measured in degrees. A right angle is 90°. Angles in a triangle sum to 180°. Angles in a quadrilateral sum to 360°.

Pythagorean Theorem

In a right triangle: a² + b² = c². The square of the hypotenuse equals the sum of the squares of the other two sides.

Tips & Tricks

Memorize the 3-4-5 and 5-12-13 Pythagorean triples for instant right-triangle problems.
The area of a circle can be found from the diameter: A = π × (d/2)² = π × d² / 4.
Angles in a polygon with n sides sum to (n−2) × 180°.
To find the area of a sector: (θ/360) × πr², where θ is the central angle in degrees.