Question

If the length of side AB of a rhombus is 10cm and diagonal is 16cm, find its area and the length of other diago​

Answer 1

Answer:

A=96cm²

a Side

10

cm

p Diagonal

16

cm

a Side

10

cm

p Diagonal

16

cm

Answer 2

⇨ Area : 96cm²

Diagonal : 6 cm

GIVEN

Side AB of a Rhombus = 10 cm

It's diagonal = 16cm

TO FIND

It's another diagonal &

Rhombus's area

CALCULATION

☆ We know that Rhomubus's sides are equal in length .

⇨ So, as AB = 10, BC = CD = DA = 10cm

Now, we have 2 isosceles triangles ( 1 rhombus )

☆ Let us find it's area

∆ ABC's area

AB = BC = 10cm & AC = 16cm

According to HERON'S Formula

s = semiperimeter

a, b, c = 3 sides of the triangle

s = (10+10+16)/2 = 18cm

Ar. = √s (s-a) (s-b) (s-c) [root for the whole]

= √18 (18-10) (18-10) (18-16)

= √18 × 8 × 8 × 2

= √2 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2 × 3 × 2 × 2 × 2

= 48cm²

We know that ∆ ABC = ∆ ADC

∴ Ar. of ∆ ABC = Ar.of ∆ ADC

48cm² = 48cm²

Area of the Rhombus = 48 + 48 = 96cm²

☆ Area of Rhombus = d1 × d2

96 = 16 × d2

96 / 16 = d2

6 = d2

∴ Diagonal 2 = 6cm

SOLUTION

Area = 96cm²

Diagonal 2 = 6cm

VERIFICATION

D1 = 16cm

D2 = 6cm

∴ Area = D1 × D2

= 16 × 6 = 96cm² ✔

☆VERIFIED☆

Hope, you got it mate

HAVE A GOOD DAY