Question

the height of an equilateral triangle is 15 cm. The area of the triangle is? ​

Answer 1

Step-by-step explanation:

ABC is EQUILATERAL TRIANGLE.

Let side = a

height = 15 cm

Construction : draw AD Perpendicular to BC.

Then, BD = DC = a/2

By pythagoras theorem,

(Height)² = (BD)² +(DC)²

(15 cm)² = (a/2)² + (a/2)²

225 cm² = a²/4 + a²/4

225 cm² = 2a²/4

225 cm² = a²/2

450 cm² = a²

a = 21.21 (approx.) cm

We get, base = 21.21 cm

We know that,

Area of equilateral triangle=root3×a²/4

= 1.732 ×(21.21)²/4

= 1.732 × 449.86/4

= 779.15/4

= 194.78 cm² (approx.)

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