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One side of a rhombus is 12 cm and one angle is 135°.a) Find the distance between the parallel sides?b) Find the area of the rhombus.No irrelevant answers needed.... |
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Answer» Given : One side of a rhombus is 12 cm and one angle is 135°. To Find : a) the distance between the parallel sides? b) the area of the rhombus. Solution: Side of Rhombus = 12 cm one angle = 135° adjacent angle = 180° - 45° Using cosine rule 4 Diagonals = √(12² + 12² - 2*12*12Cos135°) , √(12² + 12² - 2*12*12Cos45°) Cos135° = -1/√2 Cos45° = 1/√2 √(12² + 12² - 2*12*12Cos135°) = 12√(1 + 1 +√2) = 12√(2+√2) √(12² + 12² - 2*12*12Cos45°) = 12 √(2 -√2) Area of Rhombus = (1/2) * 12√(2+√2) * 12 √(2 -√2) = 72√( 4 - 2) =72√2 cm² Rhombus is parallelogram also area of Parallelogram = Base * height height = distance between the parallel sides => 72√2 = 12 * height => height = 6√2 cm distance between the parallel sides = 6√2 cm Area of Rhombus = 72√2 cm² Learn More: Is it possible to CONSTRUCT a rhombus with PQRS where pr 7CM and qs ... The area of rhombus is 360cm2 oneof it DIAGONAL is 20cm the find ... |
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