The height drawn from the top of the obtuse corner of the rhombus divides its side into 5cm and 8cm long segments

| February 9, 2021 | education

The height drawn from the top of the obtuse corner of the rhombus divides its side into 5cm and 8cm long segments, counting from the top of the acute angle. Find the areas of the parts into which the rhombus divides this height.

Determine the length of the rhombus side. AB = BC = СD = AD = AН + DН = 5 + 8 = 13 cm.

From the right-angled triangle ABН, by the Pythagorean theorem, we determine the length of the leg BН.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

BH = 12 cm.

Determine the area of the rhombus.

Savsd = AD * ВН = 13 * 12 = 156 cm2.

Determine the area of the triangle ABН.

Savn = AН * ВН / 2 = 5 * 12/2 = 30 cm2.

Then the area of the ВНDС  quadrangle will be equal to: Svnds = Savsd – Savn = 156 – 30 = 126 cm2.

Answer: The areas of the parts are 30 cm2 and 126 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.