Answer:
To find the area of the rectangle, we need to first determine the dimensions of the rectangle. We know that one side of the rectangle is the segment from G(-6, -2) to H(-3, 2), and the perimeter of the rectangle is 30 units.
The perimeter of a rectangle is given by the formula: P = 2(l + w), where l is the length and w is the width of the rectangle.
In this case, the length of the rectangle is the distance between points G and H, and the width is the distance between points G and a point on the same horizontal line as H.
First, let's find the length (L):
Distance Formula:
The distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
For points G(-6, -2) and H(-3, 2):
d = √((-3 - (-6))^2 + (2 - (-2))^2)
d = √(3^2 + 4^2)
d = √(9 + 16)
d = √25
d = 5 units
Now, we have the length (L) as 5 units.
Next, let's find the width (W):
The width is the distance between G(-6, -2) and a point on the same horizontal line as H(-3, 2). Since the x-coordinate of H is -3, the width is the absolute difference between the x-coordinates of G and H:
W = |x-coordinate of H - x-coordinate of G|
W = |-3 - (-6)|
W = |-3 + 6|
W = |3|
W = 3 units
Now, we have the width (W) as 3 units.
We can now calculate the area (A) of the rectangle:
A = Length (L) x Width (W)
A = 5 units x 3 units
A = 15 square units
So, the area of the rectangle is 15 square units.
Explanation: