One of the internal angle of a rhombus is 60° and length of its shorter diagonal is 8 cm. what is the area of the rhombus?
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Rhombus is a parallelogram with all sides equal
Also diagonal divides a parallelogram into two triangles with equal area
Given one angle of rhombus is 60° so the triangle formed is equilateral
area of an equilateral triangle is √3 ÷ 4 × a²
⇒ √3 ÷ 4 × 8 × 8 = √3 × 2 × 8 = 16√3
∴ area of a parallelogram = 2×√3 ÷ 4 × a² = 2 × 16√3 = 55.4256 cm²
Also diagonal divides a parallelogram into two triangles with equal area
Given one angle of rhombus is 60° so the triangle formed is equilateral
area of an equilateral triangle is √3 ÷ 4 × a²
⇒ √3 ÷ 4 × 8 × 8 = √3 × 2 × 8 = 16√3
∴ area of a parallelogram = 2×√3 ÷ 4 × a² = 2 × 16√3 = 55.4256 cm²
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