On a map drawn to a scale of $1 : 250000$ , a triangular plot of land has the following measurements : $A B = 3 c m, B C = 4 c m$ and $∠ A B C = 90^{\circ}$ . Calculate
(i) the actual length of $A B$ in km.
(ii) the area of the plot in sq. km:

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Solution

$A C = \sqrt{3^{2} + 4^{2}} = 5 c m$
Actual length of AC $= \frac{5 \times 250000}{100 \times 10000} k m$
$= 1.25 k m$
Actual length of AB $= \frac{3 \times 250000}{100 \times 1000} k m$
$= 0.75 k m$
Actual length of BC $= \sqrt{{1.25}^{2} - {0.75}^{2}}$
$= 1 k m$
Area $= \frac{1}{2} \times 1 \times 0.75$
$= 0.375 k m^{2}$

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On a map, drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = $90^{\circ}$ . Calculate : (i) the actual lengths of AB and BC in km. (ii) the area of the plot in sq. km.

On a map drawn to a scale of 1:2,50,000; a triangular plot of land has the following measurments : AB= 3 cm, BC= 4 cm and $∠ A B C = 90^{\circ}$ .

Calculate the actual lengths of AB and BC in km. Then the area of the plot in sq. km. is