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Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is
- a)2 : 3
- b)4 : 5
- c)5 : 6
- d)3 : 4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Corners are cut off from an equilateral triangle T to produce a regula...
The given figure can be divided into 9 regions or equilateral triangles of equal areas as shown below,
Now the hexagon consists of 6 regions and the triangle consists of 9 regions.
Hence the ratio of areas = 6/9 =2:3
Most Upvoted Answer
Corners are cut off from an equilateral triangle T to produce a regula...
Concept:
To find the ratio of areas of a hexagon and an equilateral triangle when the hexagon is formed by cutting off corners of the equilateral triangle.
Solution:
Let T be the equilateral triangle and H be the regular hexagon obtained by cutting off corners of T. Let the side length of T be ‘a’.
The area of the equilateral triangle T is given by the formula √3/4 × a².
The area of the regular hexagon H is equal to the sum of the areas of six equilateral triangles with side length a/2.
Area of each equilateral triangle = √3/4 × (a/2)² = √3/16 × a²
Area of the regular hexagon, H = 6 × √3/16 × a² = 3√3/8 × a²
Therefore, the ratio of the area of H to the area of T is:
H/T = (3√3/8 × a²) / (√3/4 × a²) = (3√3/8) × (4/3) = 2
Hence, the correct answer is option A, 2:3.
To find the ratio of areas of a hexagon and an equilateral triangle when the hexagon is formed by cutting off corners of the equilateral triangle.
Solution:
Let T be the equilateral triangle and H be the regular hexagon obtained by cutting off corners of T. Let the side length of T be ‘a’.
The area of the equilateral triangle T is given by the formula √3/4 × a².
The area of the regular hexagon H is equal to the sum of the areas of six equilateral triangles with side length a/2.
Area of each equilateral triangle = √3/4 × (a/2)² = √3/16 × a²
Area of the regular hexagon, H = 6 × √3/16 × a² = 3√3/8 × a²
Therefore, the ratio of the area of H to the area of T is:
H/T = (3√3/8 × a²) / (√3/4 × a²) = (3√3/8) × (4/3) = 2
Hence, the correct answer is option A, 2:3.
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Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T isa)2 : 3b)4 : 5c)5 : 6d)3 : 4Correct answer is option 'A'. Can you explain this answer?
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