Question

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

Answer 1

Let abcd be a rhombus.

Side of rhombus=6 cm

Altitude of rhombus=4 cm.

Area of rhombus abcd=area of triangle ABD+area of triangle BCD

=half into b×h+ half into b×h

=half ×6×4+half×6×4

=12 +12

=24 cm2

Half into d1 ×d2 =24

d1×d2=24×2

8× d2=48

d2 =48 upon 8

d2=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.