In the given figure, Δ ABC is an equilateral triangle the length of whose side is equal to 10 cm, and ΔDBC is right-angled at D and BD = 8 cm. Find the area of the shaded region. [Take: √3 = 1.732.].

Question

Philoid · Accepted Answer

Given: AB = BC = AC = a (let) = 10 cm

BD = 8 cm

Now,

Area of an equilateral triangle (∆ABC) =

=

= 25√3 cm²

= 43.3 cm²

Now, in ∆DBC

Base² + Perpendicular² = Hypotenuse²

⇒ DC² + DB² = BC²

⇒ DC² = BC²-BD²

⇒ DC² = 10²-8²

⇒ DC² = 100-64

⇒ DC² = 36 cm²

⇒ DC = 6 cm

Now,

Area of a triangle (∆DBC) = 1/2 × Base × Height

= 1/2 × DC × BC

= 1/2 × 6 cm × 8 cm

= 1/2 × 48 cm²

= 24 cm²

Now,

Area of shaded region = ∆ABC - ∆DBC

= 43.3 cm² – 24 cm²

= 19.3 cm²

In the given figure, ΔABC is an equilateral triangle the length of whose side is equal to 10 cm, and ΔDBC is right-angled at D and BD = 8 cm. Find the area of the shaded region. [Take: √3 = 1.732.].