MATHEMATICS · Multi-part · CBSE · Mathematics · Heron's Formula · Heron's Formula
Problem
A triangle has sides measuring 8cm, 11cm and 13cm. Answer the following.
(i) Define the semi-perimeter of a triangle and calculate its value for the given triangle.
(ii) State the formula that expresses the area of a triangle solely in terms of its three sides and the semi-perimeter.
(iii) For this triangle, write down the four non-zero positive factors that appear under the square-root sign when the area is evaluated by the formula stated in part (ii).
(iv) Without performing the final multiplication, explain why each of the factors obtained in part (iii) is positive.