In a four-sided field, the length of the longer diagonal is $150 m$ . The lengths of perpendiculars from the opposite vertices on this diagonal are $21 m$ and $17 m$ . Find the area of the field.

2850 m^{2}

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3522 m^{2}

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1286 m^{2}

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2652 m^{2}

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Solution

The correct option is C $2850 m^{2}$
$B D = 150 m$
$A E = 17 m$
$C F = 21 m$
Area of ABCD=area of $△ A B D +$ area of $△ B C D$
$= \frac{1}{2} B D . A E + \frac{1}{2} B D . C F$
$= \frac{1}{2} \times 150 \times 17 + \frac{1}{2} \times 150 \times 21$
$= \frac{150}{2} \times 38 = 19 \times 150 = 1900 + 950$
$= 2850 ㎡$

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In a four-sided field, the length of the longer diagonal is 150 m. The lengths of perpendiculars from the opposite vertices on this diagonal are 21 m and 17 m. Find the area of the field.

The correct option is C 2850 m2BD=150mAE=17mCF=21mArea of ABCD=area of △ABD+ area of △BCD=12BD.AE+12BD.CF=12×150×17+12×150×21=1502×38=19×150=1900+950=2850㎡

In a four-sided field, the length of the longer diagonal is $150 m$ . The lengths of perpendiculars from the opposite vertices on this diagonal are $21 m$ and $17 m$ . Find the area of the field.