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Corners of an equilateral triangle were cut off such that a regular hexagon is formed. If each side of the original triangle measures 9 cm, find the area of the hexagon in square cm.
- a)(27√3)/2
- b)(81√3)/5
- c)(81√3)/4
- d)36√3
- e)54√3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Corners of an equilateral triangle were cut off such that a regular he...
Step 1: Question statement and Inferences
Since we are not given the figure, let us draw one.
Let the equilateral triangle be ABC.
∠BAC = ∠ABC = ∠BCA = 600
The corners marked in blue are cut from this triangle, thereby resulting in a regular hexagon PQRSTU.
Let each side of this hexagon be x cm
Now, we know that
Exterior angle of a n-sided regular polygon = 360o/n
Therefore,
Exterior angle of a regular hexagon
360o/6 = 60o
This means, Angle APQ = 60o
Consider Triangle APQ:
Every angle in this triangle is 60o
Therefore, BU = UP = PA = x cm
So, BA = BU + UP + PA = 3x cm
But, we are given that
Each side of triangle ABC measures 9 cm
That is, BA = 9 cm
3x = 9 cm
x = 3 cm
Thus, we have found out that each side of the regular hexagon measures 3 cm.
We need to find the area of this regular hexagon.
Step2: Finding required values
Area of hexagon = (Area of equilateral triangle ABC) -3(Area of equilateral Triangle with side 3 cm)
Area of am equilateral triangle = 
; where a is the side of the triangle
; where a is the side of the triangleso, the area of triangle ABC = 
And, the area of each smaller triangle = 
Area of the hexagon =
Area of the hexagon =
Step 3: Calculating the final answer
So, the area of the hexagon is 
square cm.
square cm.Most Upvoted Answer
Corners of an equilateral triangle were cut off such that a regular he...
The length of each side of the regular hexagon formed by cutting off the corners of the equilateral triangle is equal to the length of the side of the original triangle.
Since the side of the original triangle measures 9 cm, each side of the hexagon measures 9 cm.
The area of a regular hexagon is given by the formula:
Area = (3√3/2) * s^2, where s is the length of each side of the hexagon.
Substituting s = 9 cm into the formula, we get:
Area = (3√3/2) * (9)^2
Area = (3√3/2) * 81
Area = (3√3/2) * 81/1
Area = (3√3 * 81)/2
Area = (3 * 9√3)/2
Area = 27√3.
Therefore, the area of the hexagon is 27√3 square cm.
The correct answer is (27).
Since the side of the original triangle measures 9 cm, each side of the hexagon measures 9 cm.
The area of a regular hexagon is given by the formula:
Area = (3√3/2) * s^2, where s is the length of each side of the hexagon.
Substituting s = 9 cm into the formula, we get:
Area = (3√3/2) * (9)^2
Area = (3√3/2) * 81
Area = (3√3/2) * 81/1
Area = (3√3 * 81)/2
Area = (3 * 9√3)/2
Area = 27√3.
Therefore, the area of the hexagon is 27√3 square cm.
The correct answer is (27).
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Corners of an equilateral triangle were cut off such that a regular hexagon is formed. If each side of the original triangle measures 9 cm, find the area of the hexagon in square cm.a)(27√3)/2b)(81√3)/5c)(81√3)/4d)36√3e)54√3Correct answer is option 'A'. Can you explain this answer?
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