Question

Find the area of a rhombus whose one side measures 5 cm and one diagonal as 8 cm.


Please solve this question

Answer 1

• Area of the Rhombus is 24cm²

According to the Question

It is given that ,

• Side of rhombus = 5cm
• Length of one diagonal ,d1 = 8cm

we have to calculate the area of rhombus .

As we know that all sides in rhombus are equal in length .

Firstly we calculate the another diagonal of rhombus .

As we know that diagonal are perpendicular bisector in rhombus . So we apply here the Pythagoras Theorem for calculating the another diagonal of the rhombus .

half of diagonal = 8/2 = 4cm

Let the another diagonal be x centimetres

➻ x² + 4² = 5² ⠀⠀⠀----(by Pythagoras Theorem)

➻ x² + 16 = 25

➻ x² = 25-16

➻ x² = 9

➻ x = √9

➻ x = 3 cm

Length of another diagonal = 2 × 3 = 6cm

Now, calculating the area of the rhombus .

• Area of Rhombus = 1/2 × d1 × d2

Putting the value we get

➻ Area of Rhombus = 1/2 × 8× 6

➻ Area of Rhombus = 1/2 × 48

➻ Area of Rhombus = 48/2

➻ Area of Rhombus = 24 cm²

• Hence the area of Rhombus is 24cm².

Answer 2

❒ Given :-

• One side of Rhombus = 5 cm
• Diagonal 1 = I cm

❒ To Find :-

• Area = ?

❒ Solution :-

⇝First finding second diagonal :

✏We know the Pythagoras theorem :

${\large{\red{\bigstar \: \: {\blue{\underbrace{\underline{\orange{\bf{A² + B² = C²}}}}}}}}}$

✏Second Diagonal :

${:{\longmapsto{\bf{A² + B² = C²}}}}$

${:{\longmapsto{\bf{A² + 5² = 8²}}}}$

${:{\longmapsto{\bf{A² + 25 = 64}}}}$

${:{\longmapsto{\bf{A² = 64 - 25}}}}$

${:{\longmapsto{\bf{A² = 39}}}}$

${:{\longmapsto{\bf{A = \sqrt{39} }}}}$

⇝Now Area :

✏We know that :

${\large{\red{\bigstar \: \: {\blue{\underbrace{\underline{\orange{\bf{area = \frac{1}{2} \times D 1 × D 2}}}}}}}}}$

✏Area :

${:{\longmapsto{\bf{Area = \frac{1}{2} \times d1 \times d2 }}}}$

${:{\longmapsto{\bf{Area = \frac{1}{2} \times 8 \times \sqrt{39} }}}}$

${:{\longmapsto{\bf{Area = \frac{1}{2} \times 8 \sqrt{39} }}}}$

➻Area = 1/2 × 49.95

➻Area = 1 × 24.975

➻Area = 24.975 or 25 cm(Approx)

⇝Therefore :

${\large{\purple{\underline{\red{\underline{\pink{\textbf{Area of Rhombus = 25cm²(approx)}}}}}}}}$

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