Question

What are the area and perimeter of the rectangle EFGH
E=(-9,-5)
F=(6,-5)
G=(6,6)
H=(-9,6)

Answer 1

To find the area and perimeter of the rectangle EFGH defined by the points E, F, G, and H, we first need to determine the lengths of its sides.

1. **Finding the Lengths of the Sides:**
- The distance between points E and F:
\[
\text{Length (EF)} = |x_F - x_E| = |6 - (-9)| = |6 + 9| = 15
\]

- The distance between points E and H:
\[
\text{Width (EH)} = |y_H - y_E| = |6 - (-5)| = |6 + 5| = 11
\]

2. **Calculating the Area:**
The area \(A\) of a rectangle is given by:
\[
A = \text{Length} \times \text{Width}
\]
Plugging in the values we found:
\[
A = 15 \times 11 = 165
\]

3. **Calculating the Perimeter:**
The perimeter \(P\) of a rectangle is given by:
\[
P = 2 \times (\text{Length} + \text{Width})
\]
Plugging in the values:
\[
P = 2 \times (15 + 11) = 2 \times 26 = 52
\]

Thus, for rectangle EFGH:
- **Area:** \(165\) square units
- **Perimeter:** \(52\) units