Question

a= (4,2)
b= (10,4)
c= (6,16)
d=(0,14)
Use the coordinates to compute the approximate area of the rectangle. Round your answer to the nearest whole number. (1 point) units2

Answer 1

To compute the area of a rectangle defined by the given coordinates, we need to identify the lengths of its sides.

The coordinates provided are:
- \( a = (4, 2) \)
- \( b = (10, 4) \)
- \( c = (6, 16) \)
- \( d = (0, 14) \)

First, we determine the minimum and maximum x-coordinates and y-coordinates from these points.

- The minimum x-coordinate is \( \min(4, 10, 6, 0) = 0 \).
- The maximum x-coordinate is \( \max(4, 10, 6, 0) = 10 \).
- The minimum y-coordinate is \( \min(2, 4, 16, 14) = 2 \).
- The maximum y-coordinate is \( \max(2, 4, 16, 14) = 16 \).

The width of the rectangle (distance between maximum and minimum x-coordinates) is:
\[
\text{Width} = \text{max x} - \text{min x} = 10 - 0 = 10
\]

The height of the rectangle (distance between maximum and minimum y-coordinates) is:
\[
\text{Height} = \text{max y} - \text{min y} = 16 - 2 = 14
\]

Now, we can calculate the area of the rectangle:
\[
\text{Area} = \text{Width} \times \text{Height} = 10 \times 14 = 140 \text{ units}^2
\]

Thus, the approximate area of the rectangle, rounded to the nearest whole number, is:
\[
\boxed{140} \text{ units}^2
\]