Question 1196859
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A kite is inscribed in a square of side 4 cm. Points X and Y are midpoints 
of the sides of the square. Find the perimeter and area of the kite.
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The kite has two opposite vertices at two opposite vertices of the square.


Two shortest sides of the kite have the length of  4/2 = 2 cm each.


The longest side is the hypotenuse of the right-angled triangle with the legs 
of 2 cm and 4 cm long, so each longest side of the kite has the length 

    {{{sqrt(2^2+4^2)}}} = {{{sqrt(20)}}} = {{{2*sqrt(5)}}}.


Thus the perimeter of the kite is  {{{2*2 + 4*sqrt(5)}}} = 12.944 cm (rounded).    <U>ANSWER</U>


To find the area of the kite, subtract the area of two triangles from the area of the original square.

You will get for the area  {{{4^2 - 2*(1/2)*2*4}}} = 16 - 8 = 8 cm^2.    <U>ANSWER</U>
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Solved.