Sector area from arc length and radius: A circle of radius 5 cm subtends an arc of length 3.5 cm. Find the area of the corresponding sector.

Introduction / Context:When arc length and radius are known, the sector area can be found without the angle by using the identity L = r * θ (θ in radians) and A = (1/2) * r^2 * θ, which combine to A = (1/2) * r * L.

Given Data / Assumptions:

• r = 5 cm
• Arc length L = 3.5 cm
• No need to convert to degrees; work directly with the relation between L and A

Concept / Approach:Use A_sector = (1/2) * r * L. This avoids computing the central angle explicitly.

Step-by-Step Solution:A = (1/2) * r * L = 0.5 * 5 * 3.5 = 8.75 sq.cms

Verification / Alternative check:Compute θ = L / r = 3.5 / 5 = 0.7 rad. Then A = (1/2) * r^2 * θ = 0.5 * 25 * 0.7 = 8.75 sq.cms, confirming the same result.

Why Other Options Are Wrong:35 and 17.5 use r*L or r^2*θ incorrectly; 55 is unrelated; 7.00 undercounts by taking 0.4 * r * L instead of 0.5 * r * L.

Common Pitfalls:Using degrees instead of radians with L = rθ; forgetting the 1/2 factor in the sector area formula.

Final Answer:8.75 sq.cms