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