Question

Find the area of rectangle BCEF. Round the area to the nearest whole number, if necessary. Please show the work

B(0,3) C(4,-1), E(2,-3), F(-2,1)

Answer 1

16 units squared

Explanation:

Area of a rectangle (A) = length (L) × width (w)

segment BF = width. Use the distance formula: w² = (x₂ - x₁)² + (y₂ - y₁)²

w² = (0 + 2)² + (3 - 1)²

w² = 2² + 2²

w² = 4 + 4

w² = 8

w = √8

w = 2√2

segment BC = length. Use the distance formula: L² = (x₂ - x₁)² + (y₂ - y₁)²

L² = (0 - 4)² + (3 + 1)²

L² = 4² + 4²

L² = 16 + 16

L² = 32

L = √32

L = 4√2

Area = L × w

= 4√2 × 2√2

= 8√4

= 8 × 2

= 16

Answer 2

Answer: 16 units²

Explanation:

Area of a rectangle (A) = length (L) × width (w)

segment BF = width. Use the distance formula: w² = (x₂ - x₁)² + (y₂ - y₁)²

w² = (0 + 2)² + (3 - 1)²

w² = 2² + 2²

w² = 4 + 4

w² = 8

w = √8

w = 2√2

segment BC = length. Use the distance formula: L² = (x₂ - x₁)² + (y₂ - y₁)²

L² = (0 - 4)² + (3 + 1)²

L² = 4² + 4²

L² = 16 + 16

L² = 32

L = √32

L = 4√2

Area = L × w

= 4√2 × 2√2

= 8√4

= 8 × 2

= 16