Question

Find the area of the kite in cm2. Round to 2 decimal places. the area?

Answer 1

The total area of the kite is `41.52` `cm^2`.

We use the sine rule, Pythagoras theorem and our big brains to solve this as shown below.

Explanation:

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 `11` `cm`, and we know that the angle which is half of angle D will be `17^o`. We know that the angle in the centre is `90^o`.

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:

`11/(sin 90)=(AE)/(sin 17)`

`AE=(11(sin 17))/(sin 90)=3.22` `cm`

Now we can use Pythagoras' theorem to find the length of DE:

`11^2=DE^2+3.22^2`

`DE=sqrt(11^2-3.2^2)=10.52` `cm`

Now the area of this lower left triangle, and the area of the lower right triangle, will be `A=(bh)/2=(3.22xx10.52)/2=16.94`, so the combined area of the lower section of the kite will be `33.88` `cm^2`.

Now for the upper left triangle, AEB. We already know the lengths of two sides, so we can just use Pythagoras:

`4^2=BE^2+3.22^2`

`BE=sqrt(4^2-3.22^2)=2.37` `cm`.

The area of this triangle is `A=(bh)/2=(2.37xx3.22)/2=3.82` `cm^2`. There are two triangles of this size, so the total area of the upper section will be `7.64` `cm^2`.

Combining the areas for the lower and upper sections, the total area of the kite will be `33.88+7.64=41.52` `cm^2`