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.

00:00 Calculate the AO side

00:03 We'll use the formula for calculating the kite area

00:06 (diagonal times diagonal) divided by 2

00:12 Let's substitute the appropriate values and solve for diagonal AC

00:33 This is the length of diagonal AC

00:39 The main diagonal in the kite intersects the secondary diagonal

00:44 And this is the solution to the question

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