Exercise $(6)$

$1-$ For the sketch below which shows boundaries of a land parcel ABC,

with right angle at $C,$ a line $GF$ is perpendicular to $AC$ divides the

parcel into two equal parts. Compute lengths of G$-$F and A$-$F$.$

Given: $A(0\mathrm{.}0$;$0\mathrm{.}0)m$;$B(50\mathrm{.}0$;$50\mathrm{.}0)m$;$C(50\mathrm{.}0$;$0\mathrm{.}0)m$;

$2-$ For the land parcel ABC given in question one above, line $DE$ is parallel to $AB$ and is to divide the land

parcel into two equal divisions. Compute lengths of lines: D$-$E$,$ B$-$D and E$-$A$.$

$3-$ The land parcel ABCD has the following recorded data about its boundaries. Lengths of sides $AB$ and $CD$

are missing. Draw a sketch showing the land parcel boundaries.

Compute lengths of sides $AB,CD$ and $AC.$

$4-$ The following figure shows the boundary of a small farm as plotted on a map of scale

$1$:$7500,$ dimensions are in cms$.$ Compute the actual ground area of the farm in sq$.$ meters, using:

$($i$)$ Average height rule,

$($ii$)$ Trapezoidal rule,

$($iii$)$ Simpson's rule

$5-$ Refer to Figure,

$=53{25}^{\text{'}}{29}^{\frac{?}{?}\text{'}}$&$=47{34}^{\text{'}}{38}^{\text{'}\text{'}}$

Control stations:

$xA=5,521\mathrm{.}25,YA=33,802\mathrm{.}48$

$xB=12,763\mathrm{.}71,YB=37,002\mathrm{.}38,$

$xC=20,450\mathrm{.}09,YC=28,861\mathrm{.}22,$

Calculate the coordinates of station $($P$).$