To find the area and perimeter of rectangle HIJK, we need to determine the lengths of the sides of the rectangle formed by the given vertices \( I, H, J, K \).
Given the vertices:
- \( I = (0, -4) \)
- \( H = (0, 4) \)
- \( J = (-4, -2) \)
- \( K = (4, -2) \)
First, we can identify the length of each side by calculating the distances between the corresponding points.
Length of Side HI:
Points \( H \) and \( I \):
- Coordinates of \( H \): \( (0, 4) \)
- Coordinates of \( I \): \( (0, -4) \)
The length \( HI \) is the absolute difference in their y-coordinates: \[ HI = |4 - (-4)| = |4 + 4| = 8 \]
Length of Side JK:
Points \( J \) and \( K \):
- Coordinates of \( J \): \( (-4, -2) \)
- Coordinates of \( K \): \( (4, -2) \)
The length \( JK \) is the absolute difference in their x-coordinates: \[ JK = |4 - (-4)| = |4 + 4| = 8 \]
Area of Rectangle HIJK:
The area \( A \) of the rectangle can be calculated using the formula: \[ A = \text{length} \times \text{width} \] Since both sides \( HI \) and \( JK \) are equal (each measuring \( 8 \)): \[ \text{Area} = 8 \times 8 = 64 \text{ square units} \]
Perimeter of Rectangle HIJK:
The perimeter \( P \) of the rectangle can be calculated using the formula: \[ P = 2 \times (\text{length} + \text{width}) \] \[ P = 2 \times (8 + 8) = 2 \times 16 = 32 \text{ units} \]
Thus, the final answers are:
- Area = 64 square units
- Perimeter = 32 units
\[ \text{Area} = 64 \text{ Square Units} \] \[ \text{Perimeter} = 32 \text{ Units} \]