Question

A diagonal of a quadrilateral is 30m in length and the perpendicular to it from opposite vertices are 6.8m and 9.6m.Find the area of the quadrilateral.

Answer 1

Solution :

Define a quadrilateral ABCD such that , one of its diagonals, say AC = 30 m .

Now , the perpendicular offsets of this quadrilateral from the opposite vertices are 6.8 m and 9.6 m.

The figure will look as shown in the attachment .

AC = 30 m .

BE = 6.8 m

DF = 9.6 m

Let us now find the area of quadrilateral ABCD

Area [ ABCD ] = Area [ ∆ BAC ] + Area [ ∆ ADC ]

=> ½ × [ AC ] × [ BE ] + ½ × [ AC ] × [ DF ]

=> ½ × [ AC ] { BE + DF }

Substituting the given values

=> ½ × 30 × 16.4

=> 15 × 16.4

=> 246 m² .

This is the required answer .

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Answer 2

Step-by-step explanation:

formula for finding area of a general quadrilateral = 1/2 x diagonal x (h1 + h2)

= 1/2 x 30 x (6.8 + 9.6)

= 1/2 x 30 x 16.4

= 246m^2