Question

find the area of an equiletral triangle whose perimeter is 45cm​

Answer 1

Answer:

91 cm square

Step-by-step explanation:

3x = 45 cm

x = 15 cm

Height of the triangle:

sin 60 = y / 15

y = 15 (sin 60) = 12.135 cm

Area = 1/2 x 15 x 12.135 = 91.0125

Approx = 91 cm square

Answer 2

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Given:

A triangle whose perimeter is 45cm.

To find:

The area of an equilateral triangle.

Explanation:

We know that perimeter of triangle= 3 × side (3a)

→ 3a = 45cm

→ a = $\cancel{\frac{45}{3} }$

→ a = 15cm

Now,

We know that formula of the area of an equilateral Δ:

→ $\frac{\sqrt{3} }{4} a^{2}$      [sq. units]

Putting the value of a in above formula, we get;

→ $\frac{\sqrt{3} }{4} *(15)^{2}$

→ $\frac{\sqrt{3} *225}{4}$

→ $\frac{\sqrt{3} *\cancel{225}}{\cancel{4}}$

→ (√3 × 56.25)cm²

→ (1.732 × 56.25)cm²           [√3= 1.732]

→ 97.425cm²

Thus,

The area of an equilateral Δ is 97.43cm².      [approx]