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A window is made up of a square portion and an equilateral triangle portion above it. The base of
the triangular portion coincides with the upper side of the square. If the perimeter of the window is
6 m, the area of the window in m2 is ___________.
the triangular portion coincides with the upper side of the square. If the perimeter of the window is
6 m, the area of the window in m2 is ___________.
- a)1.43
- b)2.06
- c)2.68
- d)2.88
Correct answer is option 'B'. Can you explain this answer?
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A window is made up of a square portion and an equilateral triangle po...
The boundary of the window is a pentagon, in which all the 5 sides are equal. As the perimeter is 6 m, each of these sides is 6/5 m.
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A window is made up of a square portion and an equilateral triangle po...
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A window is made up of a square portion and an equilateral triangle po...
To find the area of the window, we need to determine the dimensions of the square and the equilateral triangle.
Let's assume the side length of the square is "s" and the side length of the equilateral triangle is "t".
1. Perimeter of the window:
Since the perimeter of the window is given as 6 m, we can write the equation:
Perimeter of the square + Perimeter of the triangle = 6
The perimeter of the square is 4s, and the perimeter of the equilateral triangle is 3t.
So, the equation becomes:
4s + 3t = 6
2. Relationship between the side lengths of the square and the equilateral triangle:
Since the base of the triangular portion coincides with the upper side of the square, the side length of the triangle is equal to the side length of the square.
t = s
3. Solving the equations:
Substituting t = s in the equation 4s + 3t = 6, we get:
4s + 3s = 6
7s = 6
s = 6/7
Substituting the value of s back into t = s, we find:
t = 6/7
4. Area of the square:
The area of a square is given by the formula A = s^2.
So, the area of the square portion of the window is (6/7)^2 = 36/49.
5. Area of the equilateral triangle:
The formula to find the area of an equilateral triangle is A = (sqrt(3)/4) * t^2.
Substituting the value of t, the area of the triangular portion is:
A = (sqrt(3)/4) * (6/7)^2 = (9sqrt(3))/14.
6. Total area of the window:
The total area of the window is the sum of the areas of the square and the triangle:
Total area = Area of square + Area of triangle
Total area = 36/49 + (9sqrt(3))/14
Simplifying the expression, we get:
Total area = (36 + 9sqrt(3))/49
Calculating the value, we find:
Total area ≈ 2.06 m^2
Therefore, the correct answer is option B, 2.06.
Let's assume the side length of the square is "s" and the side length of the equilateral triangle is "t".
1. Perimeter of the window:
Since the perimeter of the window is given as 6 m, we can write the equation:
Perimeter of the square + Perimeter of the triangle = 6
The perimeter of the square is 4s, and the perimeter of the equilateral triangle is 3t.
So, the equation becomes:
4s + 3t = 6
2. Relationship between the side lengths of the square and the equilateral triangle:
Since the base of the triangular portion coincides with the upper side of the square, the side length of the triangle is equal to the side length of the square.
t = s
3. Solving the equations:
Substituting t = s in the equation 4s + 3t = 6, we get:
4s + 3s = 6
7s = 6
s = 6/7
Substituting the value of s back into t = s, we find:
t = 6/7
4. Area of the square:
The area of a square is given by the formula A = s^2.
So, the area of the square portion of the window is (6/7)^2 = 36/49.
5. Area of the equilateral triangle:
The formula to find the area of an equilateral triangle is A = (sqrt(3)/4) * t^2.
Substituting the value of t, the area of the triangular portion is:
A = (sqrt(3)/4) * (6/7)^2 = (9sqrt(3))/14.
6. Total area of the window:
The total area of the window is the sum of the areas of the square and the triangle:
Total area = Area of square + Area of triangle
Total area = 36/49 + (9sqrt(3))/14
Simplifying the expression, we get:
Total area = (36 + 9sqrt(3))/49
Calculating the value, we find:
Total area ≈ 2.06 m^2
Therefore, the correct answer is option B, 2.06.
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A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the window is6 m, the area of the window in m2 is ___________.a)1.43b)2.06c)2.68d)2.88Correct answer is option 'B'. Can you explain this answer?
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A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the window is6 m, the area of the window in m2 is ___________.a)1.43b)2.06c)2.68d)2.88Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the window is6 m, the area of the window in m2 is ___________.a)1.43b)2.06c)2.68d)2.88Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A window is made up of a square portion and an equilateral triangle portion above it. The base ofthe triangular portion coincides with the upper side of the square. If the perimeter of the window is6 m, the area of the window in m2 is ___________.a)1.43b)2.06c)2.68d)2.88Correct answer is option 'B'. Can you explain this answer?.
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