Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

Answer:

Lenfth of diogona=30

Length of perpendicalor=6.0and9.6

area=

$\frac{1}{2} \times length \: of \: diodonal(sum \: of \: peorpendicular)$

$\frac{1}{2} \times 30 \times (6.8 + 9.6)$

$15 \times 16.4$

$246 {cm}^{2}$