Question

Please help with this one question ASAP. (show steps if you can)

Answer 1

For this case we have that the area of the figure is given by the area of a rectangle plus the area of a square. By definition, the area of a rectangle is given by:

$A = a * b$

According to the figure we have:

$a = 9 \sqrt {2}\\b = 8 \sqrt {2} -2 \sqrt {2} = 6 \sqrt {2}$

So, the area of the rectangle is:

$A = 9 \sqrt {2} * 6 \sqrt {2} = 54 (\sqrt {2}) ^ 2 = 54 * 2 = 108$

On the other hand, the area of a square is given by:

$A = l ^ 2$

Where:

l: it is the side of the square

According to the figure we have:

$l = 2 \sqrt {2}$

So:

$A = (2 \sqrt {2}) ^ 2 = 4 * 2 = 8$

Finally, the area of the figure is:

$A_ {t} = 108 + 8 = 116$

Answer:

116