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The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

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252

m 2

250

m 2

380

m 2

347

m 2

answer is A.

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Detailed Solution

It is given the diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m.
Question Image

Consider, h1 = 13 m, h2 = 8 m and AC = 24 m
Area of quadrilateral

= 12 × b × (h 1 + h 2)

Area of triangle

= 12 × b × h

Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC.

⇒ 12 b h 1 + 12 b h 2 ⇒ 12 × 24 × 13 + 12 × 24 × 8 ⇒ 12 × 24 × (13 + 8) ⇒ 12 × 24 × 21 ⇒ 12 × 21 ⇒ 252 m 2

Therefore, area of quadrilateral ABCD is

252 m 2

.
Hence, option (1) is correct.

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