SOLUTION: A kite is inscribed in a square of side 4 cm. Points X and Y are midpoints of the sides of the sqaure. Find the perimeter and area of the kite.

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Question 1196859: A kite is inscribed in a square of side 4 cm. Points X and Y are midpoints of the sides of the sqaure. Find the perimeter and area of the kite.
Answer by ikleyn(52781) About Me  (Show Source):
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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%282%5E2%2B4%5E2%29 = sqrt%2820%29 = 2%2Asqrt%285%29.


Thus the perimeter of the kite is  2%2A2+%2B+4%2Asqrt%285%29 = 12.944 cm (rounded).    ANSWER


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%5E2+-+2%2A%281%2F2%29%2A2%2A4 = 16 - 8 = 8 cm^2.    ANSWER

Solved.