Question

On a coordinate plane, a rectangle is shown. It has points (2, 3), (4, 9), (7, 8), and (5, 2).
A rectangular table is positioned in a 10-foot by 10-foot room as shown.

How long is the longer edge of the table?

Square root of
feet

What is the area of the tabletop?

square feet

Answer 1

Take adjacent vertices in order (2,3) → (4,9) → (7,8) → (5,2). The side vectors are (2,6) and (3,−1).

Lengths: |(2,6)| = sqrt(4+36) = sqrt(40) = 2√10, |(3,−1)| = sqrt(9+1) = √10.
So the longer edge is sqrt(40) = 2√10 feet.

Area = (2√10)(√10) = 2·10 = 20 square feet.