Question

find the area of rectangle bcef. round the area to the nearest whole number, if necessary. a(-5, 4) b(0, 3) f(-2, 1) c(4, -1) e(2, -3) d(4, -5) the area is square units.

Explanation:

Step1: Find length of BC

Using distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ for points B(0, 3) and C(4, -1):
$BC = \sqrt{(4 - 0)^2 + (-1 - 3)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2}$

Step2: Find length of BF

Using distance formula for points B(0, 3) and F(-2, 1):
$BF = \sqrt{(-2 - 0)^2 + (1 - 3)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}$

Step3: Calculate area of rectangle

Area of rectangle = length × width = $BC × BF = 4\sqrt{2} × 2\sqrt{2}$
Simplify: $4×2×\sqrt{2}×\sqrt{2} = 8×2 = 16$

Answer:

16