Area of an isosceles triangle — which statements suffice? I. Perimeter of the triangle is 14 m. II. Base of the triangle is 14 m. III. Height of the triangle is 5 m.

Introduction / Context:
We must determine which statements are sufficient to compute the area of an isosceles triangle. The area formula for any triangle with a known base and corresponding height is Area = (1/2) * base * height.

Given Data / Assumptions:

• I: Perimeter = 14 m.
• II: Base = 14 m.
• III: Height = 5 m (height drawn to the base).
• Standard area formula: A = 0.5 * b * h.

Concept / Approach:
To find area directly, knowing both base (b) and corresponding height (h) is sufficient. Knowledge of perimeter alone, or perimeter with base but without height, does not directly yield height unless additional relationships are available.

Step-by-Step Solution:

Verification / Alternative check:
Perimeter information is irrelevant when both base and height are known; multiple isosceles triangles can share the same perimeter and base but differ in height if constraints are inconsistent or misread. Only II + III yields an immediate and unique area value via A = 0.5 * b * h.

Why Other Options Are Wrong:

• I and II only: Perimeter and base do not provide height; area remains indeterminate.
• I and III only: Height without knowing which side is the base (and base length) is insufficient.
• I and II only or, II and III only: The first pair (I and II) is insufficient; only the second pair works.

Common Pitfalls:
Confusing the equal sides with the base; assuming perimeter implies a unique height; using Heron's formula without all three sides.

Final Answer:
II and III only