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In fig., PQRS is a square lawn with side PQ = 42 m. Two circular flower beds are there on the sides PS and QR with center at O. the intersection of its diagonals. Find the total area of the two flower beds (shaded parts).

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788

m 2

758

m 2

504

m 2

148

m 2

answer is C.

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Detailed Solution

It is given that, PQ = 42 m.
Question Image

We have to find the total area of the two flower beds.
The expression to find the area of a triangle is

A = 12 b h

. Here b and h are the base and height of a triangle.
The diagonal of a square bisect each other at

90 o

.
Let the radius of the circle with center O is OP = OS = x. Since,

∠

POQ=

90 °

, then, by using the Pythagoras theorem, Question Image

So, area of flower bed, A is, Question Image

The total area of the two flower beds,

A r e a = 2 × A ⇒ A r e a = 2 × 252 ⇒ A r e a = 504 m 2

Therefore, the total area of the flower bed is,

504 m 2

.
Therefore, the correct option is 3.

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