Question

length of the diagonals of rhombus are 24cm and 18cm find the length of each side of the rhombus also find the area of the rhombus.​

Answer 1

Answer:

Given:- length of one diagonal = 24 cm

length of other diagonal = 18 cm

To find:- area of a rhombus

Solution:- Area of a rhombus =

1 × products of length of diagonal

2

= 1 × 24 × 18

2

= 12 × 18

= 216 cm²

Area of a rhombus = 216 cm².

Answer 2

To find : length of each side of rhombus and area of rhombus .

Given : length of diagonals of rhombus is $24\ cm$ and $18\ cm$ .

Solution :

• As per given condition we know that length of diagonals of rhombus , $24\ cm$ and $18\ cm$ .
• Let , ABCD be the rhombus . AC and BD the diagonals then ,
• AC = $24\ cm$ , BD  =$18\ cm$ .
• We know that , diagonals of rhombus bisect each other .
• Therefore , AO = OC = $12\ cm$  and OB = OD = $9\ cm$
• Let , ∠AOD = $90$ °
• Now , in ΔAOD , AO = $12\ cm$ and OD = $9\ cm$ .
• By pythagoras theorem ,
• $AD^{2}= AO^{2} +OD^{2}$

       $AD^{2} = 12^{2}+ 9^{2} \\AD^{2} = 225\\AD =15\ cm$

• Now , area of rhombus = $\frac{1}{2}\times (product \ of \ diagonals )$

                                                 $= \frac{1}{2}\times (24\times 18 ) \\= \frac{1}{2}\times 432 \\= 216\ cm^{2}$

Hence, length of each side of rhombus is $15\ cm$ and area is $216\ cm ^{2}$ .