Height of the kite is = 36 inches.
Width of the kite is = 30 inches
One of the ways to find the area is to draw a vertical line to break the kite into two equal triangles. Mark the base as 36 inches and height as 15 inches .
Now we will use the formula
to find the area of each triangle. Then we will add both the areas to find the area of the kite.
Area of 1 triangle =
= 270 square inches
Area of the 2nd triangle is also = 270 square inches
Hence, area of the kite = 270+270 = 540 square inches
When you multiply two numbers which have the same sign the answer is positive. Therefore multiply eight and three to get 24 and the answer is positive; therefor the answers 24.
So.... notice the picture below
now, we know what the "height" or "altitude" is
now, we also know the perimeter is 18cm
so, k + k + b = 18
or 2k + b = 18
thus
![\bf k=\cfrac{18-b}{2}](https://tex.z-dn.net/?f=%5Cbf%20k%3D%5Ccfrac%7B18-b%7D%7B2%7D%20)
so... one can say that
![\bf \textit{area of a triangle}=A=\cfrac{1}{2}bh\qquad \begin{cases} b=b \\\\ h=\sqrt{k^2-\left( \frac{b}{2} \right)^2} \\\\ h=\sqrt{k^2-\frac{b^2}{4}}\\ --------------\\ k=\frac{18-b}{2}\qquad thus\\ --------------\\ h=\sqrt{\left( \frac{18-b}{2} \right)^2-\frac{b^2}{4}} \end{cases}\\\\ -----------------------------\\\\ A=\cfrac{1}{2}\cdot b\cdot \sqrt{\left( \frac{18-b}{2} \right)^2-\frac{b^2}{4}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20triangle%7D%3DA%3D%5Ccfrac%7B1%7D%7B2%7Dbh%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ab%3Db%0A%5C%5C%5C%5C%0Ah%3D%5Csqrt%7Bk%5E2-%5Cleft%28%20%5Cfrac%7Bb%7D%7B2%7D%20%5Cright%29%5E2%7D%0A%5C%5C%5C%5C%0Ah%3D%5Csqrt%7Bk%5E2-%5Cfrac%7Bb%5E2%7D%7B4%7D%7D%5C%5C%0A--------------%5C%5C%0Ak%3D%5Cfrac%7B18-b%7D%7B2%7D%5Cqquad%20thus%5C%5C%0A--------------%5C%5C%0Ah%3D%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B18-b%7D%7B2%7D%20%5Cright%29%5E2-%5Cfrac%7Bb%5E2%7D%7B4%7D%7D%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0AA%3D%5Ccfrac%7B1%7D%7B2%7D%5Ccdot%20b%5Ccdot%20%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B18-b%7D%7B2%7D%20%5Cright%29%5E2-%5Cfrac%7Bb%5E2%7D%7B4%7D%7D)
and you can simplify it if you wish.. not sure you have to