Question

The length of sides of a triangular field are 32 m, 27 m and 11 m. What is the approximate area of triangle?

• A. 132 m²
• B. 142 m²
• C. 152 m²
• D. 162 m²

Answer 1

The Correct Option is B

Calculating the Area of a Triangle Using Heron's Formula

Step 1: Heron's Formula 

The area A of a triangle is given by:

A = √(s (s - a) (s - b) (s - c))

where a, b, and c are the sides of the triangle, and s is the semi-perimeter:

Step 2: Calculate the Semi-Perimeter (s)

s = (a + b + c) / 2

s = (32 + 27 + 11) / 2 = 35

Step 3: Apply Heron’s Formula

A = √(35 × (35 - 32) × (35 - 27) × (35 - 11))

= √(35 × 3 × 8 × 24)

= √20160

≈ 142 m²

Final Answer:

Thus, the correct answer is (B) 142 m².