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Find the area of segment if the values of co-ordinates are given as 119.65m, 45.76m and 32.87m. They are placed at a distance of 2 m each.
- a)20.43 sq. m
- b)2.34 sq. m
- c)20.34 sq. m
- d)87.34 sq. m
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Find the area of segment if the values of co-ordinates are given as 11...
To find the area of the segment, we need to first calculate the length of the arc and the height of the segment.
1. Finding the Length of the Arc:
The coordinates given, 119.65m, 45.76m, and 32.87m, are placed at a distance of 2m each. Therefore, the length of the arc can be calculated by summing up the distances between the coordinates:
Length of the arc = 119.65m + 45.76m + 32.87m = 198.28m
2. Finding the Height of the Segment:
The distance between each point is given as 2m. Since the segment is formed by connecting the coordinates with straight lines, the height of the segment can be calculated by finding the perpendicular distance between the chord (line connecting the endpoints of the arc) and the center of the circle.
To calculate this, we can draw a perpendicular from the center of the circle to the chord and divide it into two equal parts. This will create two right-angled triangles. The hypotenuse of each triangle is the radius of the circle, which can be calculated by dividing the length of the arc by 2π.
Radius of the circle = Length of the arc / (2π) = 198.28m / (2π) ≈ 31.58m
Now, we can calculate the height of one of the right-angled triangles using the Pythagorean theorem:
Height of the triangle = √(radius^2 - distance^2)
Height of the triangle = √(31.58m^2 - 1m^2) ≈ √992.96m^2 ≈ 31.49m
Since the segment is formed by two such triangles, the height of the segment is twice the height of one triangle:
Height of the segment ≈ 2 * 31.49m = 62.98m
3. Calculating the Area of the Segment:
The area of the segment can be calculated by subtracting the area of the triangle formed by the chord and the height of the segment from the area of the sector formed by the arc.
Area of the segment = Area of the sector - Area of the triangle
Area of the sector = (θ/360°) * π * radius^2
In this case, the angle (θ) is 120° since the three coordinates are equally spaced on the circumference of the circle.
Area of the sector = (120°/360°) * π * (31.58m)^2 ≈ 329.24m^2
Area of the triangle = (1/2) * distance * height
Area of the triangle = (1/2) * 198.28m * 62.98m ≈ 6235.34m^2
Area of the segment ≈ 329.24m^2 - 6235.34m^2 ≈ -5906.1m^2
Since the area cannot be negative, it seems there might be an error in the given values or calculations. Please double-check the data and calculations provided.
1. Finding the Length of the Arc:
The coordinates given, 119.65m, 45.76m, and 32.87m, are placed at a distance of 2m each. Therefore, the length of the arc can be calculated by summing up the distances between the coordinates:
Length of the arc = 119.65m + 45.76m + 32.87m = 198.28m
2. Finding the Height of the Segment:
The distance between each point is given as 2m. Since the segment is formed by connecting the coordinates with straight lines, the height of the segment can be calculated by finding the perpendicular distance between the chord (line connecting the endpoints of the arc) and the center of the circle.
To calculate this, we can draw a perpendicular from the center of the circle to the chord and divide it into two equal parts. This will create two right-angled triangles. The hypotenuse of each triangle is the radius of the circle, which can be calculated by dividing the length of the arc by 2π.
Radius of the circle = Length of the arc / (2π) = 198.28m / (2π) ≈ 31.58m
Now, we can calculate the height of one of the right-angled triangles using the Pythagorean theorem:
Height of the triangle = √(radius^2 - distance^2)
Height of the triangle = √(31.58m^2 - 1m^2) ≈ √992.96m^2 ≈ 31.49m
Since the segment is formed by two such triangles, the height of the segment is twice the height of one triangle:
Height of the segment ≈ 2 * 31.49m = 62.98m
3. Calculating the Area of the Segment:
The area of the segment can be calculated by subtracting the area of the triangle formed by the chord and the height of the segment from the area of the sector formed by the arc.
Area of the segment = Area of the sector - Area of the triangle
Area of the sector = (θ/360°) * π * radius^2
In this case, the angle (θ) is 120° since the three coordinates are equally spaced on the circumference of the circle.
Area of the sector = (120°/360°) * π * (31.58m)^2 ≈ 329.24m^2
Area of the triangle = (1/2) * distance * height
Area of the triangle = (1/2) * 198.28m * 62.98m ≈ 6235.34m^2
Area of the segment ≈ 329.24m^2 - 6235.34m^2 ≈ -5906.1m^2
Since the area cannot be negative, it seems there might be an error in the given values or calculations. Please double-check the data and calculations provided.
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Find the area of segment if the values of co-ordinates are given as 11...
The area of the segment can be found out by using,
A = (2/3)*(O1-(O0+O2/2)). On substitution, we get
A = (2/3)*(45.76-(119.65+32.87/2))
A = -20.34 Sq. m (negative sign has no significance)
A = 20.34 sq. m.
A = (2/3)*(O1-(O0+O2/2)). On substitution, we get
A = (2/3)*(45.76-(119.65+32.87/2))
A = -20.34 Sq. m (negative sign has no significance)
A = 20.34 sq. m.
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Find the area of segment if the values of co-ordinates are given as 119.65m, 45.76m and 32.87m. They are placed at a distance of 2 m each.a)20.43 sq. mb)2.34 sq. mc)20.34 sq. md)87.34 sq. mCorrect answer is option 'C'. Can you explain this answer?
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