Question

One side of rhombus is 8.5 cm and its altitude is 6 cm. Find the area of the rhombus.

Answer 1

Answer:

go through the above image

Answer 2

Question :-

• One side of rhombus is 8.5 cm and its altitude is 6 cm. Find the area of the rhombus.

Given :-

• One Side of Rhombus = 8.5cm
• One Diagonal of Rhombus = 6cm

To Find :-

• What is the Area of Rhombus ?

Solution :-

Firstly , we will Find the Second Diagonal of the Rhombus , then we will apply the Formula of Area of Rhombus to find the Area.

${:} \longrightarrow \sf{\bf{Side \: of \: rhombus \: = \: \: \dfrac{1}{2} \sqrt{(Diagonal 1) ^{2} \: + \: (Diagonal2)^{2} } }}$

${:} \longrightarrow \sf{\sf{8.5 \: = \: \: \dfrac{1}{2} \sqrt{6 ^{2} \: + \: (Diagonal)^{2} } }}$

${:} \longrightarrow \sf{\sf{8.5 \: \times \: 2\: = \: \sqrt{6 ^{2} \: + \: (Diagonal)^{2} } }}$

${:} \longrightarrow \sf{\sf{17 \: = \: \sqrt{6 ^{2} \: + \: (Diagonal)^{2} } }}$

${:} \longrightarrow \sf{\sf{17 ^{2} \: = \: 6 ^{2} \: + \: (Diagonal)^{2} }}$

${:} \longrightarrow \sf{\sf{17 ^{2} \: - \: 6 ^{2} \: = \: (Diagonal)^{2} }}$

${:} \longrightarrow \sf{\sf{289 \: - \: 36 \: = \: \: (Diagonal)^{2} }}$

${:} \longrightarrow \sf{\sf{253 \: = \: \: (Diagonal)^{2} }}$

${:} \longrightarrow \sf{\sf{ \sqrt{253} \: = \: \: Diagonal }}$

${:} \longrightarrow \sf{\sf \underline{\boxed{ \tt15.90 \: = \: \: Diagonal }}}$

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${:} \longrightarrow \sf{\bf{Area \: of \: rhombus \: = \: \: \dfrac{1}{2} \: \times \: Product \: of \: diagonal }}$

${:} \longrightarrow \sf{\sf{Area \: of \: rhombus \: = \: \: \dfrac{1}{2} \: \times \: 8.5 \: \times \: 15.90 }}$

${:} \longrightarrow \sf{\sf{Area \: of \: rhombus \: = \: \: \dfrac{135.15}{2} \: }}$

${:} \longrightarrow \sf{\sf \underline{\boxed{ \tt \: Area \: of \: rhombus \: = \: 67.57 {cm}^{2} \: }}}$

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So, Area of Rhombus is 67.57cm²

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