Area of a Rectangle

A rectangle is a quadrilateral in which all the four angles are right angles and the opposite sides are equal in length.

Let ABCD be a rectangle having AB = a and BC = b. Let AC be the diagonal which divides the rectangle into two right triangles, \Delta ABC and \Delta ADC.


\begin{gathered} {\text{Area  of }}\Delta ABC = \frac{1}{2}AB \times BC = \frac{1}{2}a \times b \\ \Rightarrow  {\text{Area of }}\Delta ADC = \frac{1}{2}DC \times AD = \frac{1}{2}a \times b \\ \end{gathered}

\begin{gathered} {\text{Area  of rectangle }}ABCD = {\text{Area of }}\Delta ABC + {\text{Area of }}\Delta ADC \\ \Rightarrow  {\text{Area of rectangle }}ABCD = \frac{1}{2}a \times b + \frac{1}{2}a \times b \\ \therefore  {\text{Area of rectangle }}ABCD = a \times b = {\text{length}} \times  {\text{breadth}} \\ \end{gathered}


In exchange for a square plot of land, one of whose sides is 84m, a man wants to buy a rectangular plot 144m long which is of the same area as the square plot. Find the width of the rectangular plot.


Side of the square plot  = 84m
Area of the square plot  = 84 \times 84 = 7056 square m
Length of the rectangular plot  = 144m
Length of the rectangular plot  = area of square plot
Length of the rectangular plot  = 7056 Square m
\therefore Width of rectangular plot  = \frac{{7056}}{{144}} = 49m


How many tiles 20cm square will be required to pave a footpath 1m wide carried round the outside of a grassy plot 28m long and 18m broad.



Width of foot path  = 1m
Outside dimensions of the plot are 28 + 2 = 30m and 18 + 2 = 20m
Outside area of plot PQRS = 30 \times 20 = 600 square m
Inside area of plot ABCD = 28 \times 18 = 504 square m
Area of foot path  = outside area  - inside area  = 600 - 504 = 96square m
Area of one tile  = \frac{{20}}{{100}}  \times \frac{2}{{100}} = 0.04 square m
Number of tiles required  = \frac{{96}}{{0.04}} =  2400 tiles