Question

In a four sided field, the length of the longer diagonal is 128 m. The lengths of the perpendiculars from the opposite vertices on this diagonal are 22.7 m and 17.3 m. Find the area of the field. [4 MARKS]

Answer 1

Figure: 0.5 Mark
Formula for area : 0.5 Mark
Solution: 3 Marks


It can be seen that,

Area of the field$=Area\Delta ABC+Area\Delta ADC$

Area of $\Delta ABC=\frac{1}{2}AC\times BL$

Area of $\Delta ADC=\frac{1}{2}AC\times DM$

Therefore, Area of the field
$=Area\Delta ABC+Area\Delta ADC$

$\Rightarrow \frac{1}{2}AC\times BL+\frac{1}{2}AC\times DM$

$\Rightarrow \frac{1}{2}AC[BL+DM]$

Substituting the given values, Area of the field will be

$\Rightarrow \frac{1}{2}\left(128\right)(22.7+17.3)$

$\Rightarrow \frac{1}{2}\left(128\right)\left(40\right)$

$\Rightarrow 64\times 40=2560m^2$.