Class 9: Area – Lecture Notes

$\displaystyle \textbf{Points to Remember}$

$\displaystyle \textbf{1. Equal figures: }\text{Two plane figures having equal area are called equal figures.}$

$\displaystyle \textbf{2. Congruent figures: }\text{Two plane figures having the same shape and size are}$
$\displaystyle \text{called congruent figures. But two plane figures having equal areas need not}$
$\displaystyle \text{be congruent.}$

$\displaystyle \textbf{3. Results on Area of Polygon Regions:}$

$\displaystyle \text{(i) Parallelograms on the same base and between the same parallels are}$
$\displaystyle \text{equal in area.}$

$\displaystyle \text{(ii) The area of a parallelogram is equal to the area of the rectangle on the}$
$\displaystyle \text{same base and of the same altitude, i.e. between the same parallels.}$

$\displaystyle \text{(iii) Triangles on the same base and between the same parallels are equal}$
$\displaystyle \text{in area.}$

$\displaystyle \textbf{4. Some more results:}$

$\displaystyle \text{(i) Area of a parallelogram }=\text{Base}\times\text{Height.}$

$\displaystyle \text{(ii) Area of a triangle }=\frac{1}{2}\times\text{Base}\times\text{Height.}$

$\displaystyle \text{(iii) Area of a trapezium }=\frac{1}{2}\times\text{(Sum of parallel sides)} \times\text{Height.}$

$\displaystyle \text{(iv) Area of a rhombus }=\frac{1}{2}\times\text{Product of diagonals.}$

$\displaystyle \textbf{5.}$

$\displaystyle \text{(i) If a triangle and a parallelogram are on the same base and between the}$
$\displaystyle \text{same parallels, then the area of the triangle is half of the area of the}$
$\displaystyle \text{parallelogram.}$