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There is a rectangular field of size $94 m × 32 m$ .Three roads each of 2 m width pass through the field such that two roads are parallel to the breadth of the field and the third is parallel to the length. Calculate area of the field covered by the three roads.

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228 m 2

308 m 2

328 m 2

298 m 2

answer is B.

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Detailed Solution

Given a rectangular field of size

94 m × 32 m

There is a rectangular field of size 94 m x 32 m. Three roads each of 2 m width pass through the field - Sarthaks eConnect | Largest Online Education Community

Assume, area of the field

.
As we know that, AD = KL = NM = EF = HG = BC = 32 m.
And, AB = PQ = RS = CD = 94 m.
And the width of all roads is 2 m, so TU = UI = WZ = ZY = 2m.
Area of rectangle = length

\times

breadth
The area of field covered by roads is,

⇒ x = A r . K L M N + A r . E F G H + A r . P Q R S − A r . T U V I + A r . W X Y Z

Putting values,

⇒ x = K L × L M + E F × F G + P Q × Q R − T U × U I + W Z × Z Y ⇒ x = 32 × 2 + 32 × 2 + 94 × 2 − 2 × 2 + 2 × 2

⇒ x = 64 + 64 + 188 − 4 + 4

⇒ x = 316 − 8

⇒ x = 308 m 2

Therefore, the area of field covered by roads is

308 m 2

.
Hence, option 2 is correct.

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