Find the Area of the Blades of Thc Magnetic Compass Shown in Fig.. 12.27. (Take √11 = 3.32). - Mathematics

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Find the area of the blades of thc magnetic compass shown in Fig.. 12.27. (Take √11 = 3.32).

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Solution

Area of the blades of magnetic compass = Area of ΔADB + Area of ΔCDB
Now, for area of ΔADB
Let, 2s = AD + DB + BA (Perimeter of ΔADB)

Semi perimeter (S)= `1/2(5+1+5)=11/2 cm`

By using heron’s formulae
Now, area of ΔADB `=sqrt(s(s-ad)(s-bd)(s-ba))`

`sqrt(11/2(11/2-5)(11/2-1)(11/2-5))`

`=2.49 cm^2`

= Also, area of triangle ADB = 𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝑙𝑒 𝐶𝐷𝐵
∴ Area of the blades of magnetic compass
= 2×(𝑎𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐷𝐵)
= 2 × 2.49
= `4.98 m^2`

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Chapter 17: Heron’s Formula - Exercise 17.2 [Page 20]

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RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.2 | Q 10 | Page 20

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