Question

Find the area of a rhombus whose side is 8 cm and altitude is 5.25 cm. If one of its
diagonal is 15 cm long, find the length of other diagonal.​

Answer 1

Answer:

42cm² and 5.2cm

Step-by-step explanation:

As we know rhombus is a type of parallelogram-

Area of parallelogram

= b×h

=8×5.25

=42.00cm2

Area of rhombus= 1/2× d1× d2

=42cm²= 1/2× 15× d2

=42×2/15= d2

=28/5= d2

5.2cm =d2

THANK YOU:)

Answer 2

Given:

The side of a rhombus is 8 cm and the altitude is 5.25 cm. The length of one diagonal is 15 cm.

To find:

The area of a rhombus and the length of other diagonal.

Solution:

As we know that in a rhombus ABCD having the length of two diagonals = p units and q units, the area is given by:

$= \frac{1}{2} (p \times q)$

Also,

A rhombus is a form of a parallelogram, so,

Area of rhombus

$= b \times h$

where b = base of rhombus and h = height of rhombus.

Now,

As given, we have,

Side of rhombus = 8 cm

As all sides of a rhombus are equal, so, length of the base of the rhombus = 8 cm

The altitude of rhombus = 5.25 cm

So,

Area of rhombus

$= 8 \times 5.25$

$= 42 {cm}^{2}$

Also,

Length of one diagonal = 15 cm

Let the other diagonal be 'd'.

So,

$\frac{1}{2} \times 15 \times d = 42$

On solving the above, we get

$d = \frac{42 \times 2}{15}$

$= 5.6cm$

Hence, the area of a rhombus is 42 Square centimetres and the length of one diagonal is 5.6 cm.