Question

The diagonal of a quadrilateral shaped field is 24 m and and the perpendicular dropped on it from the remaining apposite vertices are8 m . Find the area of the field

Answer 1

ANSWER:

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Let ABCD be the given quadrilateral in which
BE perpendicular to AC and
DF perpendicular to AC.

AC =24m.......given

BE=8m........given

DF=13m........given

To find :

The area of the field.
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Now we will find the area of the quad. ABCD.

So,

AREA OF QUAD. ABCD = area of Δ ABC+area
of Δ ACD.
$area \: of \: quad \: ABCD = \frac{1}{2} \: AC\times BE + \frac{1}{2} \times AC\times DF\\ \\ area \: of \: quad \: ABCD = (12 \times 8 \times 12 \times 13) {m}^{2} ..........(taking \: \frac{1}{2} or \: half \: of \: AC \: on \: both \: the \: sides) \\ \\area \: of \: quad \: ABCD = (96 + 156) {m}^{2}...........(multiplying \: 12 \: by \: 8 \: and \: 12 \: by \: 13)\\ \\ area \: of \: quad \: ABCD = 252 {m}^{2}$

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Therefore,

the area of the field is 252m^2.

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