What is the area of the rectangle below?
point A (-1,4)
point B (5,2)
point C (-4,-6)
point D (2, -7)
a. 10√6
b. 120
c. 20√13
d. 60
To find the area of a rectangle, we need the length and width of the rectangle.
Let's start by finding the length of the rectangle. To find the length, we need to find the distance between points B and C (which is a vertical line).
Using the distance formula:
length = √((5 - (-4))^2 + (2 - (-6))^2)
length = √(9^2 + 8^2)
length = √(81 + 64)
length = √145
Next, let's find the width of the rectangle. To find the width, we need to find the distance between points A and B (which is a horizontal line).
Using the distance formula:
width = √((5 - (-1))^2 + (2 - 4)^2)
width = √(6^2 + (-2)^2)
width = √(36 + 4)
width = √40
width = 2√10
Now, we can find the area of the rectangle by multiplying the length and width together:
Area = length * width
Area = √145 * 2√10 = 2√145 * √10 = 2√1450
Simplifying the final result:
Area = 2√1450
Area = 20√13
So, the area of the rectangle is c. 20√13.