Perimeter & Area: Square, Rectangle, Triangle, Polygons

Overview

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

perimeter

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 $=4\times \phantom{\rule{1ex}{0ex}}\text{side}$

Perimeter of rectangle $=2\times \phantom{\rule{1ex}{0ex}}\text{length + width}$

Perimeter of triangle $=\phantom{\rule{1ex}{0ex}}\text{sum of three sides}$

Perimeter of polygon $=\phantom{\rule{1ex}{0ex}}\text{sum of sides}$

area

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

**Area of a Square and a Rectangle** :

Area of square $={\phantom{\rule{1ex}{0ex}}\text{side}}^{2}$

Area of rectangle $=\phantom{\rule{1ex}{0ex}}\text{length}\phantom{\rule{1ex}{0ex}}\times \phantom{\rule{1ex}{0ex}}\text{width}$

**Area of a Triangle**:

$\frac{1}{2}\times \phantom{\rule{1ex}{0ex}}\text{base}\phantom{\rule{1ex}{0ex}}\times \left(height\right)$

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

Area of a triangle $=\frac{1}{2}\times \phantom{\rule{1ex}{0ex}}\text{base}\phantom{\rule{1ex}{0ex}}\times \phantom{\rule{1ex}{0ex}}\text{height}$

Area of a trapezium $=\frac{1}{2}\times \phantom{\rule{1ex}{0ex}}\text{sum of bases}\phantom{\rule{1ex}{0ex}}\times \phantom{\rule{1ex}{0ex}}\text{height}$

Area of a parallelogram $=\phantom{\rule{1ex}{0ex}}\text{base}\phantom{\rule{1ex}{0ex}}\times \phantom{\rule{1ex}{0ex}}\text{height}$

Area of a kite $=\frac{1}{2}\times \phantom{\rule{1ex}{0ex}}\text{major-diagonal}\phantom{\rule{1ex}{0ex}}\times \phantom{\rule{1ex}{0ex}}\text{minor-diagonal}$

**Area of Some Quadrilaterals** : Consider the polygon shapes as combination of triangles and find sum of area of the triangles.
$\phantom{\rule{1ex}{0ex}}\text{area of a parallelogram}\phantom{\rule{1ex}{0ex}}$$=\phantom{\rule{1ex}{0ex}}\text{base}\phantom{\rule{1ex}{0ex}}\times \phantom{\rule{1ex}{0ex}}\text{height}$
$\phantom{\rule{1ex}{0ex}}\text{area of a trapezium}\phantom{\rule{1ex}{0ex}}$$=\frac{1}{2}\times \phantom{\rule{1ex}{0ex}}\text{sum of bases}\phantom{\rule{1ex}{0ex}}\times \phantom{\rule{1ex}{0ex}}\text{height}$
$\phantom{\rule{1ex}{0ex}}\text{area of a kite}\phantom{\rule{1ex}{0ex}}$$=\frac{1}{2}\times \phantom{\rule{1ex}{0ex}}\text{product of the diagonals}$

summary

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__

Outline

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__