The sides of a triangle are 26 cm, 24 cm, and 10 cm.\nFind the area of this triangle in sq cm.

Introduction:
This question tests triangle area computation from side lengths using Heron’s formula. When height is not directly given and the triangle is not obviously right-angled (though it could be checked), Heron’s formula provides a reliable method: area = sqrt(s*(s-a)*(s-b)*(s-c)), where s is the semi-perimeter. The sides here (26, 24, 10) produce neat factors, resulting in an exact area. The problem checks whether you can compute semi-perimeter correctly and handle the multiplication under the square root without mistakes.

Given Data / Assumptions:

• Sides: a = 26 cm, b = 24 cm, c = 10 cm
• Semi-perimeter s = (a + b + c) / 2
• Heron’s formula: Area = sqrt(s*(s-a)*(s-b)*(s-c))

Concept / Approach:
Compute s first. Then compute (s-a), (s-b), (s-c). Multiply the four values and take the square root. Because the numbers factor nicely, we simplify before taking the square root to avoid large arithmetic errors.

Step-by-Step Solution:
s = (26 + 24 + 10) / 2 = 60 / 2 = 30s - a = 30 - 26 = 4s - b = 30 - 24 = 6s - c = 30 - 10 = 20Area = sqrt(30 * 4 * 6 * 20)Group terms: (30*20) * (4*6) = 600 * 24 = 14400Area = sqrt(14400) = 120

Verification / Alternative Check:
Since 10, 24, 26 is actually a right triangle set (10^2 + 24^2 = 100 + 576 = 676 = 26^2), the triangle is right-angled with legs 10 and 24. So area can also be (1/2)*10*24 = 120 sq cm. This confirms the Heron’s formula result perfectly and provides a strong consistency check.

Why Other Options Are Wrong:
108, 112, 116: usually come from wrong semi-perimeter or wrong multiplication under the square root.144: often comes from forgetting the 1/2 in the right-triangle area method.

Common Pitfalls:
Forgetting to divide perimeter by 2 for s.Making subtraction mistakes in s-a, s-b, s-c.Not recognizing simplification opportunities before taking square root.Arithmetic errors when multiplying 30*4*6*20.

Final Answer:
120 sq cm