Question

Find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.​

Answer 1

☆ Solution ☆

Given :-

• Side = 6 cm
• Altitude = 4 cm
• Diagonals = 8 cm

To find :-

• The area of rhombus
• The length of the other diagonal

Step-by-Step-Explaination :-

As we know that :-

Rhombus is also a parallelogram,

Area of parallelogram = b × h

Putting the respective value,

Area of Parallelogram = 6 × 4

Area of parallelogram = 24 cm²

Another formula for :-

Area of a rhombus = ( D1 × D2 ) / 2

Putting the respective value,

= ( 8 × D2 / 2 ) = 24

= 8 × D2 = 48

= D2 = 48/8

= D2 = 6 cm

Hence Solved !

Answer 2

Since,a rhombus is also a kind of a parallelogram.

Formula of area of rhombus =Base×Altitude

Putting values, we have

Area of rhombus =6×4=24

Since, Area of rhombus is 24 cm².

Also,formula for area of rhombus =$\frac{1}{2}×d_1d_2$

Given,Length of one diagonal =$d_1$=8

Let length of other diagonal =$d_2$

After substituting the values, we get

$24=\frac{1}{2}×8×d_2$

$24=4×d_2$

$4×d_2=24$

$d_2=\frac{24}{4}$

$d_2=6$

Hence, length of other diagonal is 6 cm.