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