Question

find the area of the 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

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Rhombus is also a parallelogram,

Area of this parallelogram,

$= b*h$

$=6*4$

$=24cm^2$

Another formula for area of a rhombus,

$= (D_1 * D_2)/2$

Given that,

$D_1 = 8cm$

So,

$(D_1*D_2)/2 = 24$

$(8*D_2)/2 = 24$

$8*D_2 = 48$

$D_2 = 48/8$

$D_2 = 6cm$

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.