The perimeter of an equilateral triangle is 6 cm. The area of the triangle is || ADRE 1.0 SLRC 2022 PAPER-III SOLVED QUESTIONS

The perimeter of an equilateral triangle is 6 cm. The area of the triangle is: 

(A) 6 cm²

(B) √6 cm²

(C) 3 cm²

(D) √3 cm²

Solution:

Given the perimeter of an equilateral triangle is 6 cm, we need to find the area of the triangle.

First, we know that the perimeter of an equilateral triangle is given by:

P=3s

where s is the length of one side of the triangle.

Since the perimeter P=6 cm, we can find the side length s as follows:

3s= 6

⇒s= 6/3

⇒s= 2 cm

Now, to find the area of an equilateral triangle, we use the formula:

Area= √3/4 × s²

⇒Area= √3/4 × (2)²

⇒Area= √3/4 × 4

⇒Area= √3 cm²

Therefore, the area of the triangle is: (D) √3 cm²

Why this question is important?

• Reinforces basic geometry concepts.
• Practices application of area and perimeter formulas.
• Common in competitive exams like ADRE SLRC.
• Enhances problem-solving skills.
• Builds foundation for advanced math topics.

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