# 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 $\Delta ADC$.

Example:

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

Solution:

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

Example:

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

Solution:

Width of foot path $= 1$m
Outside dimensions of the plot are $28 + 2 = 30$m and $18 + 2 = 20$m
Now,
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 $= 600 - 504 = 96$square 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