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√5
The basic formula is Area = base * height
EXAMPLE #1: If the given are the base/side of 10 and the height of 8, then, Area = 8*10 = 80 u²
EXAMPLE #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 u²
EXAMPLE #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 u²
EXAMPLE #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 u²
If 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 u²
EXAMPLE #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) / 2
If 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 u²
If 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 -shinnichi
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From 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/2
