Question

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

Answer 1

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`