Question

1) Find the area of a rhombus whose side is $5cm$ and whose altitude is $4.8cm$ If one of its diagonal is $48cm$ long. Find the length of the other diagonal.

2) The floor of a building consist of $3000$ tiles which are rhombus shaped and each its diagonal are $45cm$ and $30cm$ in length. Find the total cost of polishing the floor in the cost per $m^2$ is $Rs.4$.

Answer 1

1) Area of rhombus $=$base $\times$ height $=5\times 4.8=24c{m}^2$

Also area of rhombus $=\frac{1}{2}{d}_1{d}_2$

$\Rightarrow \frac{1}{2}\left(4.8\right)d_2=24$

$\Rightarrow d_2=10$cm

2)Area of one tile $=\frac{1}{2}{d}_1{d}_2=\frac{1}{2}\times 45\times 30=\frac{1350}{2}=675c{m}^2$

$\Rightarrow$ Total area of tiles $=675\times 3000=202500$ $c{m}^2$

$=20.25m^2$

$\Rightarrow$ Cost $=$Rs. $202.5\times 4=$Rs. $81$.