Given:
An umbrella is made by stitching 10 triangular pieces of cloth.
Each pieces measuring 48cm,48cm, and 30cm.
To find:
The cost of required to make umbrella at rate of 5 paisa per square cm.
Solution:
Area of a triangle is:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where,
[tex]s=\dfrac{a+b+c}{2}[/tex]
Each pieces measuring 48cm,48cm, and 30cm. So,
[tex]s=\dfrac{48+48+30}{2}[/tex]
[tex]s=\dfrac{126}{2}[/tex]
[tex]s=63[/tex]
Area of one triangular piece is:
[tex]A=\sqrt{63(63-48)(63-48)(63-30)}[/tex]
[tex]A=\sqrt{63(15)(15)(33)}[/tex]
[tex]A=\sqrt{467775}\text{ cm}^2[/tex]
[tex]A\approx 683.9408\text{ cm}^2[/tex]
Area of 10 triangular pieces is:
[tex]10\times 683.9408=6839.408\text{ cm}^2[/tex]
The rate is 5 paisa per square cm. So, the total cost is:
[tex]6839.408\times 5=34197.04[/tex]
Therefore, the total cost is 34197.04 paisa.
