ABCD- rhombus. BD is the diagonal and is equal to 15 cm. BM is the height and is equal to 12 cm.
| February 9, 2021 | education
ABCD- rhombus. BD is the diagonal and is equal to 15 cm. BM is the height and is equal to 12 cm. Find the area of the parallelogram ABCD.
From the right-angled triangle AMD, according to the Pythagorean theorem, we determine the length of the leg DM.
DM ^ 2 = ВD ^ 2 – ВM ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81.
DM = 9 cm.
Let the length of the rhombus side be X cm, then the length of the segment AM = (X – 9) cm.
In a right-angled triangle ABM, according to the Pythagorean theorem BM ^ 2 = AB ^ 2 – AM ^ 2.
12 ^ 2 = X ^ 2 – (X – 9) ^ 2.
144 = X2 – (X2 – 18 * X + 81).
18 * X = 225.
X = AB = AD = 225/18 = 12.5 cm.
Determine the area of the rhombus.
S = AD * AM = 12.5 * 12 = 150 cm2.
Answer: The area of the rhombus is 150 cm2.
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