Question

nathan has a rectangular plot of grass in his backyard that has dimensions of 2 + √2 meters in width and 6 + √3 meters in length. what is the total area of the plot of grass? recall that the area of a rectangle is the width multiplied by the length. 12 + 6√2 + 2√3 square meters 12 + 6√2 + 2√3 + √6 square meters 12 + 12√3 square meters 12 + 8√11 square meters

Explanation:

Step1: Apply area formula

$A=(2 + \sqrt{2})(6+\sqrt{3})$

Step2: Use FOIL method

$A = 2\times6+2\times\sqrt{3}+\sqrt{2}\times6+\sqrt{2}\times\sqrt{3}$
$A=12 + 2\sqrt{3}+6\sqrt{2}+\sqrt{6}$

Answer:

B. $12 + 6\sqrt{2}+2\sqrt{3}+\sqrt{6}$ square meters