Triangle area and Heron's formula

Build confidence with triangle area, Heron's formula and included-angle reasoning in this precalculus practice set. Work with two sides and an angle, three-side measurements, shared bases and composite regions. Problems connect exact calculations to geometry, scale factors, units and the limitations of inverse area data.

The questions progress from direct method selection to reconstruction and error analysis. Single-select and multiselect items include detailed worked explanations showing why a formula applies and how to check the result. Use scratch paper, retain exact values unless rounding is requested, and check that side lengths describe a nondegenerate triangle. This set follows the laws of sines and cosines and prepares you for surveying and navigation applications.