Question

the perimeter of a rhombus 100cm and one of its diagonal is 48 cm . Find its area​

Answer 1

Given :-

• perimeter of rhombus = 100 cm
• one diagonal = 48 cm

To find :-

the area of rhombus .

Formula used :-

• perimeter of rhombus = 4a
• area of rhombus = ½ d₁ × d₂
• the diagonal of rhombus = 4(a²) = (d₁)² + (d₂)²

Solution :-

perimeter of rhombus = 4a

perimeter = 100 cm

∴ 100 = 4a

a = 100/4

a = 25 cm

now, diagonal of rhombus

= 4(25)² = (48)² + (d₂)²

= 2500 = 2304 + (d₂)²

$\: \: \: \: \: \: \sf \: d₂ = \sqrt{2500 - 2304} \\ \\ \sf \: d₂= \sqrt{196} \\ \\ \sf \:d₂ \: = 14 \: cm \:$

now,

$\sf \: area \: of \: rhombus \: = \dfrac{1}{2} \: d1 \times d₂ \\ \\\sf \: area \: of \: rhombus \: = \dfrac{1}{2} \times 48 \times 14 \\ \\ \sf \: area \: of \: rhombus \: = \dfrac{1}{ \cancel2} \times ²⁴ \: \cancel{48} \times 14 \\ \\ \sf \: area \: of \: rhombus = 24 \times 14 = 336 \: {cm}^{2}$

therefore the area of rhombus = 336 cm²

additional matter about rhombus

• all side of rhombus are equal .
• a square can be called rhombus but rhombus can't be called.
• the diagonal of rhombus is not same .
• the diagonal of rhombus intersect each other at 90°
• rhombus is also known to be parallelogram because its side are parallel .