Quadrilaterals and Polygons - Coordinate Geometry Applications

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Q1. 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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Q2. 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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Q3. 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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Q4. 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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Q5. 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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Q6. What is the area of a circle with a radius of 3?

Solution:

The area of a circle is given by the formula A = πr^2. Thus, A = π * 3^2 = 9π.

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Q7. What is the perimeter of a triangle with vertices at (0, 0), (4, 0), and (0, 3)?

Solution:

The lengths of the sides are 4, 3, and 5. Perimeter = 4 + 3 + 5 = 12.

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Q8. 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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Q9. 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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Q10. 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.