Perimeter and Area in the Coordinate Plane Practice
1. Find the perimeter and area of the rectangle with vertices at (1,1), (1,4), (5,4), and (5,1).
To find the perimeter, we need to add up the lengths of all four sides of the rectangle:
Side 1: (1,1) to (1,4) has a length of 3 units.
Side 2: (1,4) to (5,4) has a length of 4 units.
Side 3: (5,4) to (5,1) has a length of 3 units.
Side 4: (5,1) to (1,1) has a length of 4 units.
Adding these lengths together, the perimeter is 3 + 4 + 3 + 4 = 14 units.
To find the area of the rectangle, we need to calculate the length of one side and the width of the rectangle:
Length: distance between (1,1) and (5,1) is 4 units.
Width: distance between (1,1) and (1,4) is 3 units.
Multiplying the length and width together, the area is 4 * 3 = 12 square units.
Therefore, the perimeter of the rectangle is 14 units and the area is 12 square units.
2. Find the perimeter and area of the triangle with vertices at (2,2), (6,4), and (4,6).
To find the perimeter of the triangle, we need to calculate the sum of the lengths of all three sides:
Side 1: (2,2) to (6,4) has a length of √20 ≈ 4.47 units.
Side 2: (6,4) to (4,6) has a length of √8 ≈ 2.83 units.
Side 3: (4,6) to (2,2) has a length of √20 ≈ 4.47 units.
Adding these lengths together, the perimeter is 4.47 + 2.83 + 4.47 ≈ 11.77 units.
To find the area of the triangle, we can use the formula for the area of a triangle given its vertices:
Area = 0.5 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
Area = 0.5 * | 2(4-6) + 6(6-2) + 4(2-4) |
Area = 0.5 * | -4 + 24 - 8 |
Area = 0.5 * | 12 |
Area = 6 square units
Therefore, the perimeter of the triangle is approximately 11.77 units and the area is 6 square units.