Quadrilaterals and Polygons - Exam Prep Problem Set

Quadrilaterals and Polygons - Coordinate Geometry Applications - Problem Set

Q. What is the area of a triangle with vertices at (1, 1), (4, 1), and (1, 5)?

Solution

Area = 1/2 * base * height = 1/2 * (4 - 1) * (5 - 1) = 1/2 * 3 * 4 = 6.

Correct Answer: A — 6

Q. What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 4), and (5, 1)?

Solution

The diagonal can be calculated using the distance formula: d = sqrt((5-1)^2 + (4-1)^2) = sqrt(16 + 9) = sqrt(25) = 5.

Correct Answer: B — 5

Q. What is the length of the side of a square with vertices at (1, 1), (1, 5), (5, 5), and (5, 1)?

Solution

The length of the side is 5 - 1 = 4.

Correct Answer: A — 4

Q. What is the perimeter of a quadrilateral with vertices at (1, 1), (1, 4), (5, 4), and (5, 1)?

Solution

Perimeter = 2 * (length + width) = 2 * (4 - 1 + 5 - 1) = 2 * (3 + 4) = 14.

Correct Answer: A — 12

Q. What is the perimeter of a regular hexagon with a side length of 3?

Solution

Perimeter = 6 * side length = 6 * 3 = 18.

Correct Answer: C — 18

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