Coordinate Geometry: Area & Perimeter Challenges for 6th Grade

A rectangle has vertices at (1, 1), (1, 4), (5, 1), and (5, 4). What is the area and perimeter of this rectangle?

• Area: 10, Perimeter: 16

• Area: 15, Perimeter: 18

• Area: 12, Perimeter: 14

• Area: 8, Perimeter: 20

A triangle has vertices at (2, 3), (4, 7), and (6, 3). Calculate the area of the triangle using the coordinates of its vertices.

• 6

• 10

• 12

• 8

A park is shaped like a trapezoid with vertices at (0, 0), (4, 0), (3, 3), and (1, 3). What is the area of the park?

• 12

• 9

• 15

• 6

A square is plotted on the coordinate plane with one vertex at (2, 2) and the opposite vertex at (6, 6). What is the perimeter of the square?

• 8

• 20

• 12

• 16

A rectangular garden has corners at (0, 0), (0, 8), (6, 0), and (6, 8). If a path of 1 unit width is built around the garden, what is the new perimeter of the garden including the path?

• 24 units

• 30 units

• 40 units

• 36 units

A triangle has vertices at (1, 1), (1, 5), and (4, 1). What is the perimeter of the triangle?

• 15

• 8

• 12

• 10

A rectangular swimming pool is located at (2, 2), (2, 7), (7, 2), and (7, 7). If the pool is filled with water to a depth of 2 feet, what is the volume of water in cubic feet?

• 70 cubic feet

• 50 cubic feet

• 100 cubic feet

• 30 cubic feet

A parallelogram has vertices at (1, 1), (4, 1), (5, 4), and (2, 4). What is the area of the parallelogram?

• 15

• 9

• 12

• 6

A rectangular field has its corners at (0, 0), (0, 10), (15, 0), and (15, 10). If a fence is built around the field, what is the total length of the fence?

• 40 units

• 30 units

• 50 units

• 60 units

A trapezoid has vertices at (1, 1), (4, 1), (3, 4), and (2, 4). Calculate the area of the trapezoid using the coordinates of its vertices.

• 3.5

• 7.5

• 5.0

• 10.5