Deltoid Geometry: Calculate CO Given AO=6cm, BO=5cm, and Area=80cm²

To solve for $CO$, we will use the area formula for the deltoid:

• Step 1: Calculate full length of diagonal $BD$:

$BD = 2 \times BO = 2 \times 5 = 10 \text{ cm}$.

• Step 2: Use the kite area formula:

• $\text{Area} = \frac{1}{2} \cdot AC \cdot BD$.

Substitute known values into the formula:

$80 = \frac{1}{2} \cdot (6 + CO) \cdot 10$.

Step 3: Simplify and solve for $CO$:

$80 = 5 \cdot (6 + CO)$ leads to

$80 = 30 + 5CO$.

Solving for $CO$, we subtract 30 from both sides:

$50 = 5CO$,

$CO = \frac{50}{5} = 10$.

Therefore, the side $CO$ is 10 cm.