Area of triangle ABC?

A normal-level "Area" problem."See 30°, halve the slanted side." Knowing this one fact turns it into a 10-second problem.

Hints

The area of a triangle is base × height ÷ 2. First choose the base. We know BC = 12 cm, so let's use that.
The height is the perpendicular distance from A down to BC. Call the foot H and draw a dotted line. Once we know this length, we are done.
Look at the blue triangle ABH. Angle B is 30°, angle H is 90°. The three angles add to 180°, so angle A is 180 − 30 − 90 = 60°.
A 30°-60°-90° right triangle is half of an equilateral triangle. To see it, fold the triangle down using BC as a mirror.
After folding, angle B is 30° twice, so 60°. AB and A′B are the same length because one is the fold of the other. Two equal sides with 60° between them means an equilateral triangle, so all three sides are 8 cm.
So AA′ = 8 cm, and BC cuts AA′ exactly in half. Therefore height AH = 8 ÷ 2 = 4 cm.
Base 12 cm, height 4 cm. Now just apply the formula: 12 × 4 ÷ 2.

Answer 24cm²