Question

Find the area of a rhombus given that its side measures 13 cm and one of diagonals measures 10 cm.
The area of a rhombus is 441 cm and its perimeter is 84 cm. Find is altitude.
The base of a triangular park is 420 m and its altitude is 325 m. Find the cost of
levelling the park at the rate of 15 per 1000 m​

Answer 1

Answer:

Step-by-step explanation:

ANSWER

(i) Given

Side of rhombus =13 cm

Length of diagonal AC=10 cm

∴ OC=5 cm

Since, the diagonals of a rhombus bisect each other at right angles.

So, △BOC is right-angled.

Then, by Pythagoras Theorem we have

BC  

2

=OC  

2

+OB  

2

 

⇒13  

2

=5  

2

+OB  

2

 

⇒OB  

2

=169−25=144

⇒OB=  

144

​  

=12cm

Hence,

diagonal BD=2×OB=2×12=24 cm

(ii) Area of rhombus =  

2

1

​  

×d  

1

​  

×d  

2

​  

=  

2

1

​  

×10×24=12 cm  

2