The height drawn from the top of the obtuse corner of the rhombus divides the side into 6 cm and 4 cm

The height drawn from the top of the obtuse corner of the rhombus divides the side into 6 cm and 4 cm segments from the top of the acute corner. Find the area of the rhombus.

Since the height divides the side into segments 4 cm and 6 cm long, the side of the rhombus is equal to their sum – 10 cm.

Consider a right-angled triangle formed by the drawn height, the side of the rhombus, and the portion of the side lying between the acute angle and the base of the height.

The ratio of the adjacent leg to the hypotenuse is equal to the cosine of the angle, which means 6/10 = cos α, where α is the acute angle of the rhombus.

It is known that cos2 α + sin2 α = 1, then sin α = √ (1 – cos2 α) = √ (1 – 0.62) = √0.64 = 0.8.

The area of the rhombus is determined by the formula: S = a2 * sin α = 102 * 0.8 = 100 * 0.8 = 80 cm2.