Question

area of triangle =?

Explanation:

Step1: Identify the figure

The figure is a square \(ABCD\) with side length \(AB = 6\) cm (since \(AB\) is given as 6 cm and \(ABCD\) is a square, \(AB = BC = CD = DA = 6\) cm). The triangle in question is \(\triangle ACD\) or \(\triangle ABC\)? Wait, no, looking at the diagram, the shaded triangle is \(\triangle AOC\)? Wait, no, actually, in a square, the area of \(\triangle ABC\) or \(\triangle ADC\) can be calculated. Wait, the base and height of the triangle: for a triangle with base \(AB = 6\) cm and height \(BC = 6\) cm? Wait, no, the triangle here: actually, in a square, the area of \(\triangle ABC\) is \(\frac{1}{2} \times AB \times BC\). Since \(AB = 6\) cm and \(BC = 6\) cm (because \(ABCD\) is a square with side 6 cm), so:

Step2: Calculate the area

The formula for the area of a triangle is \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\). Here, the base can be \(AB = 6\) cm and the height can be \(BC = 6\) cm (since \(BC\) is perpendicular to \(AB\)). So:

\[
\text{Area} = \frac{1}{2} \times 6 \times 6
\]

\[
\text{Area} = \frac{1}{2} \times 36 = 18
\]

Wait, alternatively, if the triangle is \(\triangle ACD\), but no, looking at the diagram, the triangle is \(\triangle ABC\) or \(\triangle AOC\)? Wait, no, the key is that in a square, the area of the triangle formed by two adjacent sides and the diagonal? Wait, no, actually, the triangle here: the base is \(AB = 6\) cm, and the height is equal to the side of the square, which is 6 cm. So the area is \(\frac{1}{2} \times 6 \times 6 = 18\) square centimeters.

Answer:

The area of the triangle is \(18\) square centimeters (or \(18\ \text{cm}^2\)).