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Answer 1

By pythagoreans' theorem,

Longer edge
= √(2² + 6²)
= √40

∴ The length of the longer edge is the square root of 40 feet.

Shorter edge
= √(1² + 3²)
= √10

Area = L × B
= √40 × √10
= 20 feet²

Answer 2

A(2, 3); B(4, 9); C(7, 8); D(5, 2)

1. How long is the longer edge of the table?
$AB= \sqrt{(x_b-x_a)^2+(y_b-y_a)^2} = \sqrt{(4-2)^2+(9-3)^2}= \\ = \sqrt{2^2+6^2}= \sqrt{4+36}= \sqrt{40} \ \text{feet}$

2. What is the area of the tabletop?
$BC= \sqrt{(x_c-x_b)^2+(y_c-y_b)^2} = \sqrt{(7-4)^2+(8-9)^2}= \\ = \sqrt{3^2+(-1)^2}= \sqrt{9+1}= \sqrt{10} \ \text{feet} \\ \\ Area=AB*BC= \sqrt{40}* \sqrt{10}= \sqrt{400}= 20 \ \text{square feet}$

Answer: √40; 20.