# The side of a square is x meters. the midpoints of the sides are joined another square whose area is 16m. find the value of x and the area of the portion of the bigger square that is outside the smaller square

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Lets say there is a square, then place 4 points on the midpoint of each side. Now connect the dots of the midpoint... which will result like a square but it looks more of a diamond. Then calculate each side with 45 45 90. So if you think, the area of the diamond shaped square if 16m, use the formula.

A=s²

16 m=s²

Square root both sides

s=4 m

Now, the opposite side of the 90 degrees has a side length of 4 m, now use the 45, 45, 90 angle theorem, which states that the opposite side of the 45 is equal to the length of the opposite side of 90 divided by the square root of 2.

The opposite side of 90 (the length) is 4 m

4 m/√2 = 2√2

Therefore the value of x is 2√2, now that is only half of the side, so double it you have 4√2 m.

Find the area of the bigger square:

A=s²

A=(4√2 m)²

A=32 m²

A=s²

16 m=s²

Square root both sides

s=4 m

Now, the opposite side of the 90 degrees has a side length of 4 m, now use the 45, 45, 90 angle theorem, which states that the opposite side of the 45 is equal to the length of the opposite side of 90 divided by the square root of 2.

The opposite side of 90 (the length) is 4 m

4 m/√2 = 2√2

Therefore the value of x is 2√2, now that is only half of the side, so double it you have 4√2 m.

Find the area of the bigger square:

A=s²

A=(4√2 m)²

A=32 m²