The base of the perpendicular of the rhombus lowered from the top of the obtuse angle to its side
| July 22, 2021 | education
The base of the perpendicular of the rhombus lowered from the top of the obtuse angle to its side divides it into a segment of 16 and 10 cm starting from the apex of the obtuse angle. Find the area of a rhombus.
Determine the length of the segment AD.
AD = AH + DH = 10 + 16 = 26 cm.
Since ABCD is a rhombus, the lengths of all its sides are equal, AB = BC = CD = AD = 26 cm.
The ВН segment is perpendicular to AD, therefore, ВН is the height of the rhombus, and the ABН triangle is rectangular.
By the Pythagorean theorem, we determine the length of the BH leg.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 676 – 100 = 576.
BH = 24 cm.
Determine the area of the rhombus.
Savsd = AD * BH = 26 * 24 = 624 cm2.
Answer: The area of the rhombus is 624 cm2.
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