Question

Shown below is the trophy shield Akshi received on winning an international Table tennis tournament.

The trophy is made of a glass sector DOC supported by identical wooden right triangles ∆ DAO and ∆ COB. Also, AO = 7 cm and AO : DA = 1 ∶ √3 (Use √3 = 1.73)

Based on the given information, answer the following questions:

(i) Find ∠DOC

(ii) Find the area of the wooden triangles

(iii) Find the area of the shape formed by the glass portion OR If Akshi wants to decorate the boundary of the glass portion with glitter tape, then find the length of the tape she needs.

Answer 1

(i) Let ∠DOA =θ, 

then tanθ = AD/AO = √3/1

⟹ θ= 60°

∠DOA = ∠COB = 60°

∠DOC = 180° − (60° + 60°) = 60°

(ii) Area of two wooden triangles = 2 ×1/2 × 7 × 7√3 = 84.77 cm²

(iii) AD/AO = cos 60° 

⟹7/DO = 1/2

⟹ DO = 14 cm

Area of sector DOC = 60/360 × π × 142 = 102.67 cm²

OR

AO/DO = cos 60° 

⟹7/DO = 1/2

⟹ DO = 14 cm

Length of tape required = 2 × 14 + 60/360 × 2 × π × 14 = 42.67 cm