Calculate AO Length in Kite ABCD: Given Area 42 cm² and Diagonal 14 units

Question

The kite ABCD shown below has an area of 42 cm².

AB = BC

DC = AD

BD = 14

The diagonals of the kite intersect at point 0.

Calculate the length of side AO.

00:16 Let's calculate the length of side AO.

00:19 We'll use the kite area formula.

00:22 It's diagonal one times diagonal two, divided by two.

00:28 Now, substitute the given values to find diagonal AC.

00:49 This gives us the length of diagonal AC.

00:55 Remember, the main diagonal intersects the secondary diagonal.

01:00 And that's how we solve this problem. Great job!

We substitute the data we have into the formula for the area of the kite:

$S=\frac{AC\times BD}{2}$

$42=\frac{AC\times14}{2}$

We multiply by 2 to remove the denominator:

$14AC=84$

Then divide by 14:

$AC=6$

In a rhombus, the main diagonal crosses the second diagonal, therefore:

$AO=\frac{AC}{2}=\frac{6}{2}=3$

3 cm