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Q1. If a rectangle has vertices at (1, 1), (1, 4), (5, 1), and (5, 4), what is its area?
Solution:
The area of a rectangle is given by the formula: Area = length * width. The length is 5 - 1 = 4 and the width is 4 - 1 = 3. Thus, Area = 4 * 3 = 12.
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Q2. What is the circumference of a circle with a radius of 5 units?
Solution:
The circumference of a circle is given by the formula: C = 2πr. Here, r = 5, so C = 2π * 5 = 10π.
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Q3. What is the length of the line segment connecting the points (2, 3) and (2, 7)?
Solution:
The length of a vertical line segment is the difference in the y-coordinates. Here, length = 7 - 3 = 4.
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Q4. What is the perimeter of a triangle with sides of lengths 3, 4, and 5?
Solution:
The perimeter of a triangle is the sum of the lengths of its sides. Here, Perimeter = 3 + 4 + 5 = 12.
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Q5. What is the area of a square with a side length of 7 units?
Solution:
The area of a square is given by the formula: A = side². Here, A = 7² = 49.
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Q6. What is the area of a square with vertices at (1, 1), (1, 5), (5, 1), and (5, 5)?
Solution:
The area of a square is given by Area = side². The side length is 5 - 1 = 4, so Area = 4² = 16.
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Q7. What is the area of a trapezoid with bases of lengths 6 and 10, and a height of 4?
Solution:
The area of a trapezoid is given by the formula: A = 0.5 * (base1 + base2) * height. Here, A = 0.5 * (6 + 10) * 4 = 0.5 * 16 * 4 = 32.
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