Question

2if perimeter of Rhombus is 100 cm
length of one diagonal is 48cm find the
area of Rhombus.​

Answer 1

$\bf{Answer}$

Concept :-

Here they have given perimeter of rhombus and one diagonal they have given perimeter means we can find side of a rhombus and We know one diagonal We can also find other diagonal then by using Perimeter of rhombus formula We can find area of rhombus

Formulae used :-

• Perimeter of rhombus = 4x
• Area of rhombus = 1/2 diagonal -1 × diagonal -2

Solution :-

Finding side of a rhombus :-

In rhombus all sides are equal since, four sides are equal Perimeter is nothing but sum of sides

So, x+ x + x + x = 4x

4x = 100cm

$\sf\dfrac{100}{4}$ = x

x = 25cm

Since side of a rhombus is 25cm

Finding the other diagonal :-

Refer the attachment (diagram -1 )

Already As we know one of the diagonal is 48cm

Lets draw a two diagonal with point O

Diagonals of rhombus AC,BD

diagonal 1 ,

AC = 48 cm i.e

AO + OC = 48cm

AO = OC (properties of diagonal )

AO = OC = 24cm

Also we know BO = OD

Now , If you observe the rhombus It divides into 4 right angle triangles

In a triangle AOD (picture-2)

AO = 24cm (opposite side )

AD = 25cm (Hypotenuse)

We can find OD by using pythagoras theorem (adjacent side)

AO² + OD² = AD²

(24)² + x² = (25)²

576 + x² = 625

x² = 625 - 576

x² = 49

x = 7cm

Adjacent side = 7cm = OD

OD = OB = 7cm

Since diagonal-2 = 7+7cm

Diagonal-2 = 14cm

Now,

We know

Diagonal 1 = 48cm

Diagonal 2 = 14cm

Finding area of rhombus

Area of rhombus = 1/2 $\sf{d_1 \times d_2}$

Area = 1/2 × 48cm × 14cm

Area = 24cm × 14cm

Area = 336cm²

So, area of rhombus = 336cm²

Know more :-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²