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?

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)   (Show Source): You can put this solution on YOUR website!

given:
a square of side of
and are midpoints of the side of a square
if so, then diagonals ( and ) of the kite are equal length as a side of a square

then the area is:

Answer by ikleyn(52866)   (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.
~~~~~~~~~~~~~~~~

            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 = = . Thus the perimeter of the kite is = 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 = 16 - 8 = 8 cm^2. ANSWER

Solved.

RELATED QUESTIONS
A kite inscribed in a square of side 4cm. Points X and Y are midpoints of the sides of a... (answered by ikleyn)
A kite is inscribed in a square of side 4cm. points x and y are midpoints of the sides of (answered by ikleyn)
A kite is inscribed in a square of side 4 cm. Points X and Y are midpoints of the sides... (answered by ikleyn,fractalier)
A kite is inscribed in a square of side 4 cm. Points X and Y are midpoints of the sides... (answered by ikleyn,Timnewman)
A kite is inscribed in a square of side 4 cm. Points X and Y are midpoints of the sides... (answered by ikleyn)
A kite is inscribed in a square of side 4 cm. Points X and Y are midpoints of the sides... (answered by josgarithmetic)
Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides.... (answered by ikleyn)
A kite has an 8-inch side and a 15-inch side, which form a right angle. Find the length... (answered by MathLover1)
Find the area of a circle inscribed in a square of side 28... (answered by math_helper)