maths > mensuration-high

Perimeter & Area: Square, Rectangle, Triangle, Polygons

    what you'll learn...


Finding perimeter and area of simple figures (squares, rectangle, triangle, polygon) are revised without much discussion.


The word "perimeter" means: measure around a shape. Perimeter is from the Greek root words peri (around) and meter (measure).

Length is the distance-span between two points.

Perimeter :
Perimeter of a figure is the length of the line or curve forming the boundary of the figure.

Perimeter of square =4× side

Perimeter of rectangle =2× length + width

Perimeter of triangle = sum of three sides

Perimeter of polygon = sum of sides perimeter


Area of a figure is the "surface-span within a closed shape".

Area of a Square and a Rectangle :
Area of square = side2

Area of rectangle = length × width area of rectangle

Area of a Triangle:
12× base ×(height) area of a triangle

Area of a Polygon : Consider a polygon to be combination of known geometrical forms, mostly triangles.area of a polygon The geometrical forms and the formula for area are:

Area of a triangle =12× base × height

Area of a trapezium =12× sum of bases × height

Area of a parallelogram = base × height

Area of a kite =12× major-diagonal × minor-diagonal

Area of Some Quadrilaterals : Consider the polygon shapes as combination of triangles and find sum of area of the triangles.area of parallelogram area of a parallelogram = base × height area of trapezium area of a trapezium =12× sum of bases × height area of kite area of a kite =12× product of the diagonals


This is covered in Mesuration-Basics in the following pages

  →   Perimeter of Polygons

  →   Area of Square & rectangle

  →   Area of Triangle

  →   Area of Polygons

  →   Perimeter & Area of Quadrilaterals


The outline of material to learn Mensuration : Length, Area, and Volume is as follows.

Note 1: click here for the detailed overview of Mensuration High

Note 2: click here for basics of mensuration, which is essential to understand this.

•  Basics of measurement

  →   Summary of Measurement Basics

  →   Measurement by superimposition

  →   Measurement by calculation

  →   Measurement by equivalence

  →   Measurement by infinitesimal pieces

  →   Cavalieri's Principle (2D)

  →   Cavalieri's Principle (3D)

•  Perimeter & Area of 2D shapes

  →   Circumference of Circles

  →   Area of Circles

•  Surface area & Volume of 3D shapes

  →   Prisms : Surface Area & Volume

  →   Pyramids : Surface Area & Volume

  →   Cone : Surface Area & Volume

  →   Sphere : Surface Area & Volume

•  Part Shapes

  →   Understanding part Shapes

  →   Circle : Sector and Segment

  →   Frustum of a Cone