From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

Question

Philoid · Accepted Answer

Area of equilateral side of side ‘a’ =

We divide the triangle in three triangles,

Area of triangle = (1/2 × a × 14) + (1/2 × a × 10) + (1/2 × a × 6)

Area of triangle = 1/2 × a × (14 + 10 + 6)

= 1/2 × a × 30

⇒ cm

Area (Δ) =

⇒ Area (Δ) =

⇒ Area(Δ) = 300√3 cm²