To find the area of a kite, the formula is:
[tex]A=\frac{d_1d_2}{2}[/tex]
This means that we need to find the lengths of the diagonals. We can use the Pythagorean Theorem for this.
Let's first solve for the length of d1.
[tex]\begin{gathered} x^2+x^2=11^2 \\ 2x^2=121 \\ x^2=\frac{121}{2} \\ x=\frac{11\sqrt{2}}{2} \end{gathered}[/tex]
Because the d1 is twice the length of x, then
[tex]d_1=2(\frac{11\sqrt{2}}{2})=11\sqrt{2}\approx15.6[/tex]
Now we solve for d2.
Again, we use the Pythagorean Theorem.
[tex](\frac{11\sqrt{2}}{2})^2+y^2=61^2[/tex][tex]\begin{gathered} y^2=61^2-(\frac{11\sqrt{2}}{2})^2 \\ \\ y^2=\frac{7,321}{2} \\ \\ y\approx60.5 \end{gathered}[/tex]
So d2 = 2y = 121.
To find the area, we multiply the diagonals then divide by 2.
[tex]A=\frac{15.6(121)}{2}=943.8[/tex]
The area is approximately 943.8 square units.
The perimeter is much easier to find. We simply add all of the sides.
We know that a kite has 2 pairs of consecutive sides that are congruent.
So the perimeter is 11 + 11 + 61 + 61 or 144 units.
