Question

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

Answer 1

Given that side of the rhombus = 6cm.

Given that Altitude of the rhombus = 4cm.

We know that Area of the rhombus = Base * Altitude

                                                            = 6 * 4

                                                            = 24cm^2.


Let the length of the other diagonal = xcm.

We know that Area of the rhombus = 1/2 * d1 * d2
 
                                    24 = 1/2 * 8 * x

                                    24 = 4 * x

                                    24/4 = x

                                      6 = x.


Therefore the length of the other diagonal = 6cm.



Hope this helps!

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.