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Q1. What is the area of a polygon with vertices at (0, 0), (4, 0), (4, 3), (0, 3)?
Solution:
This is a rectangle with length 4 and width 3. Area = length * width = 4 * 3 = 12.
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Q2. What is the length of the side of a square with vertices at (1, 1), (1, 5), (5, 1), and (5, 5)?
Solution:
Length of side = 5 - 1 = 4.
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Q3. What is the length of the side of a square if its area is 64?
Solution:
The area of a square is given by side^2. Thus, if area = 64, then side = √64 = 8.
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Q4. What is the area of a rectangle with vertices at (1, 2), (1, 5), (4, 2), and (4, 5)?
Solution:
The length is 4 - 1 = 3 and the width is 5 - 2 = 3. Area = length * width = 3 * 3 = 9.
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Q5. What is the area of a regular hexagon with a side length of 4?
Solution:
The area of a regular hexagon can be calculated using the formula A = (3√3/2) * side^2. Thus, A = (3√3/2) * 4^2 = 48.
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Q6. What is the area of a rhombus with diagonals of lengths 10 and 6?
Solution:
Area = (d1 * d2) / 2 = (10 * 6) / 2 = 30.
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Q7. What is the area of a parallelogram with base 10 and height 5?
Solution:
The area of a parallelogram is calculated as base times height. Thus, area = 10 * 5 = 50.
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Q8. If a parallelogram has vertices at (2, 3), (5, 3), (6, 1), and (3, 1), what is its area?
Solution:
Base = 5 - 2 = 3, Height = 3 - 1 = 2. Area = base * height = 3 * 2 = 6.
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Q9. What is the area of a trapezoid with bases of lengths 5 and 7, and a height of 4?
Solution:
Area = 1/2 * (base1 + base2) * height = 1/2 * (5 + 7) * 4 = 24.
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Q10. What is the length of the diagonal of a rectangle with width 6 and height 8?
Solution:
The length of the diagonal can be found using the Pythagorean theorem: d = √(width^2 + height^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10.
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