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hodyreva [135]
3 years ago
5

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

Mathematics
1 answer:
mihalych1998 [28]3 years ago
7 0

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

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