"Construct a triangle ABC with AB = 5 cm, BC = 6 cm and angle $B = 60°$ and find its area"

Step 1: Draw the base and angle

First, we draw the base of the triangle, which is the line segment BC of length 6 cm. Then, at vertex B, we construct an angle of 60 degrees using a protractor or compass, as this angle is given.

Step 2: Mark point A

From point B, along the ray of the 60-degree angle, we measure and mark point A such that the length of AB is 5 cm. Finally, we connect point A to point C to complete the triangle ABC.

Step 3: Calculate the area of the triangle

To find the area of the triangle, we use the formula that involves two sides and the sine of the included angle. Here, the sides are AB and BC, and the included angle is B.

Step 4: Substitute and simplify

We substitute the value of $\sin(60^\circ) = \frac{\sqrt{3}}{2}$ into the formula and perform the multiplication to get the final area of the triangle.

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