Question

Find the height and hence the area of equilateral triangle with the side 6.4cm.

Answer 1

Let ABC be the equilateral triangle of side 6.4cm.

Now,

Let us draw a perpendicular to AM from the base BC such that it joints the point A.

Now,

We know,

This perpendicular bisects the base BC into two equal parts.

So,

BM = MC

Or BM = MC = 6.4/2 = 3.2cm

In equilateral triangle,

∠A =∠B =∠C = 60°

So ∠A/2 =∠B/2 =∠C/2 = 60°/2 = 30°

We know,

sinθ = AC/AM

Or sin30° = 6.4/AM

Or 1/2 = 6.4/AM

Or AM = 12.8 cm

Now,

ar(ABC) = 1/2 × BC × AM = 1/2 × 6.4 × 12.8 = 40.96 cm²