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The vertices of a shaded square are the midpoints of the sides of square ABCD. The length of the diagonal of square ABCD is 6 inches.

The Vertices Of A Shaded Square Are The Midpoints Of The Sides Of Square ABCD The Length Of The Diagonal Of Square ABCD Is 6 Inches class=

Sagot :

mlarsen5000

Answer:

A=13.47 in.

P=14.68 in.

Step-by-step explanation:

First, we have to figure out the sides of square ABCD. The diagonal forms the hypotenuse of a right equilateral triangle.

a²+a²=6²

2a²=36

a²=18

a=√18

a=4.24

Half of 4.24 would be the distance From each corner of ABCD to the neighboring midpoints.  (2.12)

2.12²+2.12²=c²

4.49+4.49=c²

13.48=c²

√13.48=c

3.67=c

Now that we know each side of the shaded square, we can get the area and perimeter.

A=3.67x3.67=13.47

P=3.67x4=14.68

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