Find the area of an acute-angled triangle with a height of 7 cm if the height divides the opposite

Find the area of an acute-angled triangle with a height of 7 cm if the height divides the opposite side into 3 cm and 9 cm segments.

The area of a triangle is half the product of the base and the height. In triangle ABC

AH – the height drawn to the base of the speaker;

The height divides the base into 3 cm and 9 cm segments, which means:

AC = AH + HC = 3 + 9 = 12 (cm);

AH = 7 cm;

Area of triangle ABC:

S = 1/2 AC * AH = 1/2 * 12 * 7 = 42 (cm²).