The height BH of the rhombus ABCD divides its side AD into segments AH = 4 and HD = 1. Find the area of the rhombus

bystudin | May 31, 2020 | Education

The area of the rhombus is S = ah, where a is the side of the rhombus, h is the height of the rhombus.
AD = AH + HD = 4 + 1 = 5.
AD = AB = BC = CD (by definition of a rhombus).
Consider the triangle ABH.
ABH is rectangular (because BH is height), then by the Pythagorean theorem: AB ^ 2 = BH ^ 2 + AH ^ 2
5 ^ 2 = BH ^ 2 + 4 ^ 2
25 = BH ^ 2 + 16
BH2 = 9
Bh = 3
S diamond = AD * BH = 5 * 3 = 15
Answer: S diamond = 15

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.