Question

In ΔOPQ, o = 4.3 cm, p = 4.5 cm and q=5.6 cm. Find the area of ΔOPQ to the nearest square centimeter.

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Answer 1

`\qquad \textit{Heron's area formula} \\\\ A=√(s(s-o)(s-p)(s-q))\qquad \begin{cases} s=(o+p+q)/(2)\\[-0.5em] \hrulefill\\ o = 4.3\\ p = 4.5\\ q = 5.6\\ s=(4.3+4.5+5.6)/(2)\\ \qquad 7.2 \end{cases} \\\\\\ A=√(7.2(7.2-4.3)(7.2-4.5)(7.2-5.6)) \\\\\\ A=√(7.2(2.9)(2.7)(1.6)) \implies A\approx√(90.2016)\implies A\approx 9~cm^2`