Question

Find the area of rhombus one side of which measures 20cm and one of whose diagonals is 24 cm​

Answer 1

Answer:

A=384cm²

Step-by-step explanation:

Answer 2

The area of the rhombus is $\bold{384\mathrm{cm}^{2}}$

Given:

• One side of a rhombus = 20cm and one diagonal = 24 cm

To Find:

• The area of a rhombus

Solution:

In the rhombus ABCD,

Let, AB = 20 cm

And AC = 24 cm

From the diagram,

AO + CO = 24 cm

AO = 12 cm [∵ AO = CO]

In $\Delta \mathrm{AOB},$

AB = 20 cm and AO= 12 cm

Using Pythagoras Theorem,

$\mathrm{BO}=\sqrt{20^{2}-12^{2}}\ \mathrm{cm}$

$=\sqrt{400-144}\ \mathrm{cm}$

$=\sqrt{256}\ \mathrm{cm}$

$=16\ \mathrm{cm}$

Hence,

• BO = DO = 16 cm

∴ BD = 16 cm + 16 cm = 32 cm.

Area of Rhombus

$=\frac{1}{2} \times \text { Diagonal } 1 \times \text{ Diagonal } 2$

$=\frac{1}{2} \times A C \times B D$

$=\frac{1}{2} \times 24\ \mathrm{cm} \times 32\ \mathrm{cm}$

$=384\ \mathrm{cm}^{2}$