Question

find the area of a rhombus whose side is 6.5 cm and altitude is 5 cm . if one of its diagonal is 13 cm long find the length of other diagonal

Answer 1

Heya..

Since rhombus is also a parallelogram.

Since Area of a llgm = base*height

Hence Area of a rhombus also equal to base * height

=) Area of a rhombus = 6.5cm* 5cm

=) Area of rhombus = 32.5 cm^2.

Since Area of a rhombus = 1/2 * d1 * d2

=) 1/2 * d1 * d2 = 32.5 cm^2

=) 1/2 * 13cm * d2 = 32.5 cm^2

=) 6.5 cm * d2 = 32.5 cm^2

=) d2 = 32.5 / 6.5

=) d2 = 5cm.

Hope it's helpful to u.

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 =6.5×5=32.5

Since, Area of rhombus is 32.5 cm².

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

Given,Length of one diagonal =$d_1$=13

Let length of other diagonal =$d_2$

After substituting the values, we get

$32.5=\frac{1}{2}×13×d_2$

$32.5=6.5×d_2$

$6.5×d_2=32.5$

$d_2=\frac{32.5}{6.5}$

$d_2=5$

Hence, length of other diagonal is 5 cm.