In a four sided field, the length of the longer diagonal is 128 m. The lengths of the perpendiculars from the opposite vertices on this diagonal are 22.7 m and 17.3 m. Find the area of the field.

2460

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2560

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3460

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2840

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Solution

The correct option is B 2560

Area of △ ABC = $\frac{1}{2}$ AC×BL

Area of △ ADC = $\frac{1}{2}$ AC×DM

Area of the field = Area △ ABC + Area △ ADC

⇒ $\frac{1}{2}$ AC×BL+ $\frac{1}{2}$ AC×DM

⇒ $\frac{1}{2}$ AC [BL+DM]

Substituting the given values, Area of the field

⇒ $\frac{1}{2}$ (128)(22.7 + 17.3)

⇒ $\frac{1}{2}$ (128) (40)

⇒ 64×40 = 2560 $m^{2}$ .

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In a four sided field, the length of the longer diagonal is 128 m. The lengths of the perpendiculars from the opposite vertices on this diagonal are 22.7 m and 17.3 m. Find the area of the field.

The correct option is B 2560 Area of △ ABC = 12 AC×BL Area of △ ADC = 12 AC×DM Area of the field = Area △ ABC + Area △ ADC ⇒ 12 AC×BL+ 12 AC×DM ⇒ 12 AC [BL+DM] Substituting the given values, Area of the field ⇒ 12 (128)(22.7 + 17.3) ⇒ 12 (128) (40) ⇒ 64×40 = 2560 m2.