Question

The area of a rhombus with diagonals of lengths 7cm and 12cm is _______ cm²
options A::46,,,B::42,,C::480,,D::14​

Answer 1

Given:-

• Diagonals of lengths of a rhombus is 7 cm and 12 cm.

⠀

To find:-

• Area of a rhombus.

⠀

Solution:-

Here,

• D1 = 7 cm
• D2 = 12 cm

⠀

★Formula used:-

Area of rhombus = ½ × D1 × D2

⠀

⇛ ½ × D1 × D2

⇛ ½ × 7 × 12

⇛ ½ × 84

⇛ 42 cm²

⠀

Hence,

• the area of a rhombus is 42 cm².

⠀

Therefore,

• Option (b) is correct.

⠀

⛦More Formulas:-

→ Area of rectangle = length × breadth sq.units

→ Perimeter of square = 4 × side units

→ Area of square = side × side sq.units

→ Perimeter of circle = 2πr units

→ Area of circle = πr² sq.units

→ Perimeter of parallelogram = 2 × (a + b) units

→ Area of parallelogram = base × height sq.units

→ Perimeter of rhombus = 4 × side units

→ Area of rhombus = 1/2 × diagonal (1) × diagonal (2) sq.units

→ Perimeter of equilateral triangle = 3 × side units

→ Area of equilateral triangle = √3/4 × a² = 1/2 × side × height sq.units

→ Perimeter of trapezoid = (Sum of all sides) units

→ Area of trapezoid = 1/2 × height × (sum of parallel sides) sq.units

Answer 2

Correct Question:-

The area of a rhombus with diagonals of lengths 7cm and 12cm is _______ cm²

A::46 cm²

B::42 cm²

C::480 cm²

D::14. cm²

Given:-

• Diagonal 1 = 7 cm
• Diagonal 2 = 12 cm

To Find:-

• Area of Rhombus

Solution:-

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \mathfrak{ \underline{ \green{Formula \: to \: calculate \: the \: area \: of \: Rhombus}}}$

$\boxed{ \mathfrak{ \purple{ \star \: \: \: \: \: { \red{ \large{area = \frac{1}{2} \times daigonal1 \times diagonal2}}}}}}$

According to question,

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \: \: area = \frac{1}{ \cancel2} \times 7 \times \cancel 12}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \: \: area = 7 \times 6}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \purple{ \mathfrak{ area = 42 \: {cm}^{2} }}}}}$

Hence:-

• The area of Rhombus is 42 cm²

$\therefore \sf{ \underline{ \orange{The \: correct \: option \: is \: (B)}}}$