Find the area of the kite in cm2. Round to 2 decimal places. the area?
The total area of the kite is
We use the sine rule, Pythagoras theorem and our big brains to solve this as shown below.
If we draw in the lines AC and BD the kite becomes 4 right-angled triangles. Call the point where those lines cross E.
The lower left triangle is AED. We know that side AD is the same length as side CD, which is
We want to find the lengths of the lines AE and DE: once we know those it will be easy to calculate the area of triangle AED and triangle CED has the same area.
Use the sine rule:
Now we can use Pythagoras' theorem to find the length of DE:
Now the area of this lower left triangle, and the area of the lower right triangle, will be
Now for the upper left triangle, AEB. We already know the lengths of two sides, so we can just use Pythagoras:
The area of this triangle is
Combining the areas for the lower and upper sections, the total area of the kite will be