Question

Find the area of a rhombus whose diagonals are 14cm and 36cm

Answer 1

Answer:

Step-by-step explanation:

Area of rhombus=1/2d1d2

D1=14;de=36

1/2×14×36

=14×18

=252

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Answer 2

ANALYSIS:-

Given:

• The length of a diagonal of a rhombus is 14 cm.
• The length of its another diagonal is 36 cm.

To find:

• The area of the rhombus.

CONCEPT:

‎ ‎ ‎ ‎ ‎ ‎As per the analysis, the concept on which the question is based is "Mensuration". This concept is a branch of Mathematics that deals with the computation of geometric magnitudes, such as the the perimeter of a surface, the area of a surface and the volume of a solid.

A rhombus is a parallelogram in which all sides are equal and it's diagonals bisects each other at right angles.

• Perimeter = 4 (side) units
• Area = ½ × (product of the diagonals)

SOLUTION:

Let the first diagonal be d₁ and the second diagonal be d₂.

So,

• d₁ = 14 cm
• d₂ = 36 cm

According to the question, it's area has to be found.

$\small \underline{ \boxed{ \sf{ \pmb{Area_{(rhombus)} = \frak{ \dfrac{1}{2}\times (product \: of \: the \: diagonals)\:sq.units}}}}}$

On substituting the values,

$\longmapsto{ \sf{ \dfrac{1}{2} \times (d1 \times d2) }} \\ \\ \longmapsto{ \sf{ \dfrac{1}{2} \times (14 \times 36)}} \\ \\ \longmapsto{ \sf{ \dfrac{1}{ \cancel{2}} \times ( \cancel{504})}} \\ \\ \longmapsto{ \sf{1 \times 252}} \\ \\ \longmapsto \boxed{ \tt{ \pmb{ \red{252 \: {cm}^{2} }}}}$

$\\ \therefore \underline{ \cal{ \pmb{The \:area \: of \:the \: rhombus \: is \: \frak{\orange{252 \: {cm}^{2} }. }}}}$

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SOME FORMULAE RELATED TO THE CONCEPT:

• Area of rectangle = Length × Breadth sq.units
• Area of square = (Side)² sq.units
• Area of parallelogram = Base × Height sq.units
• Area of triangle = ½ × (Base × Height) sq.units
• Area of trapezium = ½ × (Sum of parallel sides) × Height sq.units
• Area of circle = πr²
• Area of circular annulus = π(R² – r²) sq.units
• Volume of cube = (Side)³ cu.units
• Volume of cuboid = Length × Breadth × Height sq.units
• Volume of sphere = 4/3 πr³ cu.units

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