question_answer

If each side of the rhombus is 40 m and its longer diagonal is 48 m, then the area of rhombus is____.

A) \[~1536\,{{m}^{2}}\]                         

B) \[~1636\,{{m}^{2}}\] 

C) \[~1236\,{{m}^{2}}\]             

D)        \[~1336\,{{m}^{2}}\] 

Correct Answer: A

Solution :

Here, each side of rhombus = 40 cm. One of the diagonal = 48 m a = 40, b = 40, c = 48 \[s=\frac{a+b+c}{2}=\frac{40+40+48}{2}=\frac{128}{2}=64\,m\] Area of triangle I \[=\sqrt{64(64-40)(64-40)(64-48)}\] \[=\sqrt{64(24)(24)(16)}\] \[=768\,{{m}^{2}}\] Similarly, area of triangle \[||=768\,{{m}^{2}}\] So, So, area of rhombus \[=768\,{{m}^{2}}+768\,{{m}^{2}}\] \[=15.36\,{{m}^{2}}\]