The area (in cm²) of an equilateral triangle of side 91 cm is:

Appeared in: DSSSB October 2024

Explanation

The area of an equilateral triangle is calculated using the specific formula: Area = (√3/4) × a², where 'a' represents the side length.
In this problem, the given side length (a) is 91 cm.
First, square the side length: a² = 91 × 91 = 8281.
Next, substitute this value into the formula: Area = (√3/4) × 8281.
This simplifies to the final expression: 8281√3 / 4 cm², which corresponds to the correct option.

Option A: This option incorrectly uses a denominator of 6. The correct formula for the area of an equilateral triangle always uses a denominator of 4.
Option B: This option incorrectly uses a denominator of 3. The constant in the area formula is √3/4, not √3/3.
Option C: This option incorrectly uses a denominator of 2. This might arise from confusing the area formula with the formula for the height of an equilateral triangle, which is h = (√3/2) × a.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Area of an equilateral triangle as background academic context rather than a clinical decision trigger.
This question tests foundational mathematical aptitude, which is a component of the non-nursing syllabus for many nursing entrance examinations.
While not a direct clinical skill, proficiency in basic mathematics is essential for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting data from medical charts and reports.
What if the question asked for the perimeter? The perimeter would be much simpler to calculate: P = 3 × side = 3 × 91 = 273 cm. It's important not to confuse the formulas for area and perimeter.

How to Approach the Question

First, identify the geometric shape mentioned in the question, which is an 'equilateral triangle'.
Next, recall the specific formula for the area of this shape. For an equilateral triangle, the formula is Area = (√3/4) × side².
Identify the value provided for the 'side' of the triangle, which is 91 cm.
Substitute this value into the formula: Area = (√3/4) × 91².
Perform the calculation: 91² equals 8281. The expression becomes (√3/4) × 8281.
Finally, rewrite the expression as 8281√3 / 4 and compare it with the given options to select the correct one.

Concept Tested & Keywords

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Practise the full DSSSB October 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.