TUTORIAL: GETTING THE AREA OF A RHOMBUS
Refer to the figure.
s = side = b = base = 10
h = height = 8
d_1 = diagonal 1 = 4√5
d_2 = diagonal 2 = 8√5
dif = difference of two diagonals = 4√5The basic formula is
Area = base * heightEXAMPLE #1:
If the given are the base/side of 10 and the height of 8, then,
Area = 8*10 = 80 u²EXAMPLE #2:
If the given are the two diagonals of 4√5 and 8√5, then,
Area = (d_1 * d_2) / 2
Area = (4√5)(8√5)/2
Area = (4)(8)(5)/2
Area = 80 u²EXAMPLE #3:
If the given are the side of 10 and the difference of two diagonals of 4√5, then,
Area = s² - (dif/2)²
Area = 10² - (4√5/2)²
Area = 100 - (2√5)²
Area = 100 - 20
Area = 80 u²EXAMPLE #4:
If the given are the height of 8 and either of the diagonals (either 4√5 or 8√5), then,
Area = d²h / 2√(d² - h²)If the given diagonal is 4√5, then,
Area = (4√5)²(8) / 2√[(4√5)² - 8²]
Area = (80)(4) / √(80 - 64)
Area = (80)(4) / √16
Area = (80)(4) / 4
Area = 80 u²If the given diagonal is 8√5, then,
Area = (8√5)²(8) / 2√[(8√5)² - 8²]
Area = (320)(4) / √(320 - 64)
Area = (320)(4) / √256
Area = (320)(4) / 16
Area = 80 u²EXAMPLE #5:
If the given are the side of 10 and either of the diagonals (either 4√5 or 8√5), then,
Area = d√(4s² - d²) / 2If the given diagonal is 4√5, then,
Area = (4√5)√[4(10²) - (4√5)²] / 2
Area = (2√5)√(400 - 80)
Area = (2√5)√320
Area = (2√5)(8√5)
Area = (2)(8)(5)
Area = 80 u²If the given diagonal is 8√5, then,
Area = (8√5)√[4(10²) - (8√5)²] / 2
Area = (4√5)√(400 - 320)
Area = (4√5)√80
Area = (4√5)(4√5)
Area = (4√5)²
Area = 80 u²#MMBLTutorial
-shinnichiFrom the comment section!
Example #6.
Cut the rhombus, to have 2 triangles.... In the figure use the diagonal AC... You'll get triangles ADC & ABC... AREA of triangle is bh/2ADC: 10*8/2=40u^2
ABC: 10*8/2=40u^2
ABCD=ABC+ADCABCD=80u^2