The figure above shows a rectangular plot of land OPQR. In this plot, a patch of land OABO, where the path AB represents a circular arc of radius 20andradic;2 metres, is developed as a lawn. The point A is at a distance of 20 metres each from sides OR and OP. The point B is at a distance of 10andradic;6 metres from side OP and 10andradic;2 metres from side OR. What is the area, in square metres, of the intended lawn?a)b)c)d)e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?

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The figure above shows a rectangular plot of land OPQR. In this plot, a patch of land OABO, where the path AB represents a circular arc of radius 20√2 metres, is developed as a lawn. The point A is at a distance of 20 metres each from sides OR and OP. The point B is at a distance of 10√6 metres from side OP and 10√2 metres from side OR. What is the area, in square metres, of the intended lawn?

a)
b)
c)
d)
e)
Cannot be determined

Correct answer is option 'B'. Can you explain this answer?

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The figure above shows a rectangular plot of land OPQR. In this plot, ...

Given:

Let’s consider OP as the x-axis and OR as the y-axis.
So, the coordinates of points A and B are: A(20, 20) and B(10√2, 10√6)

To find: Area of region OABO

Approach:

We’re given that AB is a circular arc of radius 20√2 meters but we are not told that region OABO represents a sector of a circle of radius 20√2 meters. So, it will be wrong to assume that OA and OB are the radii of the sector OABO. In fact, we’ll need to find the values of OA and OB to check if they are indeed the radii of circular arc AB.
1. We can find the value of OA and OB using the Pythagoras theorem in triangles OEA and OFB.
If OA and OB are indeed the radii of the circular arc, then we can use the formula of area of sector to find the area of region OABO. But to find this area, we’ll also need the measure of ∠BOA. We can find this angle as follows

- ∠BOA = ∠BOF - ∠AOE
  - ∠BOF can be found by applying trigonometric ratios in ΔOFB

Working Out:

Thus, we see that OA = OB = Radius of the circular arc AB =20√2 meters

This means that OABO is indeed the sector of a circle of radius 20√2 meters
So, we’ll be able to apply the formula for area of a sector to answer the question.

Thus, ∠BOA = 15^o

Finding the area of sector OABO

So, the area of sector

Looking at the answer choices, we see that the correct answer is Option B

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The figure above shows a rectangular plot of land OPQR. In this plot, a patch of land OABO, where the path AB represents a circular arc of radius 20√2 metres, is developed as a lawn. The point A is at a distance of 20 metres each from sides OR and OP. The point B is at a distance of 10√6 metres from side OP and 10√2 metres from side OR. What is the area, in square metres, of the intended lawn?a)b)c)d)e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The figure above shows a rectangular plot of land OPQR. In this plot, a patch of land OABO, where the path AB represents a circular arc of radius 20√2 metres, is developed as a lawn. The point A is at a distance of 20 metres each from sides OR and OP. The point B is at a distance of 10√6 metres from side OP and 10√2 metres from side OR. What is the area, in square metres, of the intended lawn?a)b)c)d)e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The figure above shows a rectangular plot of land OPQR. In this plot, a patch of land OABO, where the path AB represents a circular arc of radius 20√2 metres, is developed as a lawn. The point A is at a distance of 20 metres each from sides OR and OP. The point B is at a distance of 10√6 metres from side OP and 10√2 metres from side OR. What is the area, in square metres, of the intended lawn?a)b)c)d)e)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.

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