Question

Given rectangle ABCD with vertices A(1, 4), B(3, 6), C(6, 3), and D(4, 1), what is the area of ABCD? Leave your answer in simplified radical form.

Answer 1

• 12 units²

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Find the length of two adjacent sides, AB and AD, then multiply them together to get the area.

Use distance formula:

• 
  `AB=√((3-1)^2+(6-4)^2) =√(2^2+2^2) =√(2*2^2)=2√(2)`

• 
  `AD=√((4-1)^2+(1-4)^2) =√(3^2+(-3)^2) =√(2*3^2)=3√(2)`

The area is:

• Area = AB*AD

• Area =
  `2√(2) *3√(2)`

• Area = 6(2)

• Area = 12