Question

use the diagram to find the perimeter and the area of rectangle bcef. round your answers to the nearest hundredth if necessary.
the perimeter is □ units.
the area is □ square units.
(diagram shows coordinates: a(-5, 4), b(0, 3), f(-2, 1), c(4, -1), e(2, -3), d(4, -5) on a coordinate grid)

Explanation:

Step1: Find length of BC

Coordinates of B(0, 3) and C(4, -1). Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
$BC = \sqrt{(4 - 0)^2 + (-1 - 3)^2} = \sqrt{16 + 16} = \sqrt{32} = 4\sqrt{2} \approx 5.66$

Step2: Find length of BF

Coordinates of B(0, 3) and F(-2, 1). Use distance formula.
$BF = \sqrt{(-2 - 0)^2 + (1 - 3)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \approx 2.83$

Step3: Calculate perimeter of rectangle

Perimeter of rectangle = $2\times( length + width ) = 2\times(BC + BF)$
$= 2\times(4\sqrt{2} + 2\sqrt{2}) = 2\times(6\sqrt{2}) = 12\sqrt{2} \approx 16.97$

Step4: Calculate area of rectangle

Area of rectangle = $length \times width = BC \times BF$
$= 4\sqrt{2} \times 2\sqrt{2} = 8\times2 = 16$

Answer:

The perimeter is $\boldsymbol{16.97}$ units.
The area is $\boldsymbol{16}$ square units.