Question

d c o a 6 cm b p area of triangle =?

Explanation:

Step1: Identify equal base & height

We know that triangle $AOC$ and triangle $ABC$ share the same base $AC$, and their heights from $O$ and $B$ to $AC$ are equal (since $OB$ is parallel to $AC$ as $OB$ is a radius of the circle tangent to $BC$ and $AB$, making $OB \perp AB$, and $BC \perp AB$ in the square, so $AC$ and $OB$ are parallel). Thus, $S_{\triangle AOC} = S_{\triangle ABC}$.

Step2: Calculate area of $\triangle ABC$

The side length of the square is $6$ cm. The area of $\triangle ABC$ is half the area of the square.
$S_{\triangle ABC} = \frac{1}{2} \times 6 \times 6$

Answer:

$18$ cm²