Ch 10 introduces Heron's formula — a method to find the area of a triangle when all three sides are known, without needing the height. The formula extends to finding areas of quadrilaterals by dividing them into triangles.
For a triangle with sides a, b, c: semi-perimeter s = (a+b+c)/2. Area = √[s(s−a)(s−b)(s−c)]. This formula works for any triangle including scalene, where finding the height is difficult.
To find the area of a quadrilateral using Heron's formula: divide it into two triangles using a diagonal, find the area of each triangle using Heron's formula, and add them together.
Download: https://ncert.nic.in/textbook/pdf/iemh110.pdf | Complete book: https://ncert.nic.in/textbook/pdf/iemh1ps.zip
Heron's formula is most useful when you know all three sides but not the height (altitude). This is common in surveying and real-world measurements where measuring height directly is impractical.
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