Question

find the area of a rhombus whose side is 6 cm and whose altitude is 4 cm. if one of the diagonal is 8 cm long find the length of the other diagonal

Answer 1

{½ diagonal}²= side²--{½ diagonal}²
= Altitude²= side² -- Altitude²
=6²--4²= 36—12=20
Altiftude=4√2
So,diagonal 1=8√2
Area= ½×8√2=16√2 sq.cm

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.