A quadrilateral has an area of 453.6 cm². The length of a diagonal is 42 cm and the perpendicular distance from one vertex is 10 cm. Find the perpendicular distance from the other vertex (in cm).
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Solution

Area of a quadrilateral can be written as the sum of two triangles.

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Let the perpendicular distance from the other vetex be x
Therefore, area of field = Ar of $Δ$ ADC + Ar of $Δ$ ABC
$\Rightarrow$ 453.6 $c m^{2}$ = $\frac{1}{2}$ × 42 × 10 + $\frac{1}{2}$ × 42 × x
$\Rightarrow$ x = 11.6 cm

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A quadrilateral has an area of 453.6 cm2. The length of a diagonal is 42 cm and the perpendicular distance from one vertex is 10 cm. Find the perpendicular distance from the other vertex (in cm). __

Area of a quadrilateral can be written as the sum of two triangles. . Let the perpendicular distance from the other vetex be x Therefore, area of field = Ar of Δ ADC + Ar of Δ ABC ⇒ 453.6cm2 = 12 × 42 × 10 + 12 × 42 × x ⇒ x = 11.6 cm

A quadrilateral has an area of 453.6 cm². The length of a diagonal is 42 cm and the perpendicular distance from one vertex is 10 cm. Find the perpendicular distance from the other vertex (in cm).
__

Area of a quadrilateral can be written as the sum of two triangles.

.

Let the perpendicular distance from the other vetex be x
Therefore, area of field = Ar of $Δ$ ADC + Ar of $Δ$ ABC
$\Rightarrow$ 453.6 $c m^{2}$ = $\frac{1}{2}$ × 42 × 10 + $\frac{1}{2}$ × 42 × x
$\Rightarrow$ x = 11.6 cm