SOLUTION: A kite inscribed in a square of side of 4cm. Points X and Y are midpoints of the side of a square . Find the area of a kite . What is its parameter?

Algebra ->  Parallelograms -> SOLUTION: A kite inscribed in a square of side of 4cm. Points X and Y are midpoints of the side of a square . Find the area of a kite . What is its parameter?       Log On


   

Question 1196795: A kite inscribed in a square of side of 4cm. Points X and Y are midpoints of the side of a square . Find the area of a kite . What is its parameter?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


given:
a square of side of 4cm
X+and Y are midpoints of the side of a square
if so, then diagonals (p and q) of the kite are equal length as a side of a square

then the area is:
A=%28pq%29%2F2=%284cm%2A4cm%29%2F2=8m%5E2


Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.
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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            I consider other location of vertices than @MathLover1,
            in order for the shape was a real kite and not a square. 


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.