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ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle?
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ABCD is a square of side a cm baby, BC, CD and AD all are the cause of...
Given Information:
- ABCD is a square with side length a cm.
- BC, CD, and AD are chords of circles with equal radii.
- The chords subtend an angle of 120 degrees at their respective centers.
To find:
- The total area of the given figure where arcs are part of the circle.
Analysis:
- Since the chords are radii of the circles, they are equal in length.
- The angle subtended by each chord at the center of the circle is 120 degrees.
- The arc length subtended by 120 degrees in a circle is (120/360) * 2πr = (1/3) * 2πr = (2/3)πr.
Calculation:
- The total area of the figure consists of 4 identical segments, each formed by an arc and a triangle.
- The area of each segment is the sum of the area of the sector and the area of the triangle.
- The area of the sector is (2/3)πr^2, and the area of the triangle can be found using trigonometry.
- The triangle is an equilateral triangle with side length a, formed by two radii and a chord.
- The height of the triangle can be found using the Pythagorean theorem: h = √(a^2 - (a/2)^2) = √(3a^2/4) = a√3/2.
- The area of the triangle is (1/2) * base * height = (1/2) * a * (a√3/2) = a^2√3/4.
- The total area of each segment is (2/3)πr^2 + a^2√3/4.
- The total area of the figure is 4 times the area of each segment, which is 4*((2/3)πr^2 + a^2√3/4) = (8/3)πr^2 + 4a^2√3.
Therefore, the total area of the given figure where arcs are part of the circle is (8/3)πr^2 + 4a^2√3.
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ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle?
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ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle?.
ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a square of side a cm baby, BC, CD and AD all are the cause of circles with equal radii each if the chords substance and angle of 120 degrees at the respected centres find the total area of the given figure where arc are part of the circle?.
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