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....
Answers
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
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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