Question

The perimeter of an equilateral triangle is 48 cm. Its area is

(a)18√3 sq. cm

(b) 72√3 sq. cm

(c)64√3 sq. cm

(d) 60√3 sq. cm

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Answer 1

GivEn:

• Perimeter of equilateral triangle is 48 cm

To find:

• Area of equilateral triangle

SoluTion:

We know that measure of all sides of an equilateral triangle is equal.

So, Let the side of equilateral triangle be x cm.

We know that,

✇ Perimeter of ∆ = Sum of measure of its all sides

Here, Perimeter of triangle is 48 cm.

Therefore,

↠ 48 = x + x + x

↠ 48 = 3x

↠ x = 48/3

↠ x = 16 cm

━━━━━━━━━━━━━━━━━━━━━━━

★ Now, Finding area of Equilateral triangle,

Formula to find,

✇ Area of Equilateral triangle = √3/4 × (a)²

where, a is the sides of Equilateral triangle.

Now, Putting value in formula,

➯ √3/4 × (16)²

➯ √3/4 × 256

➯ √3 × 64

➯ 64√3 cm²

∴ Area of given Equilateral triangle is 64√3 cm².