Question

In ΔDEF, d = 98 cm, e = 35 cm and f=97 cm. Find the area of ΔDEF to the nearest 10th of a square centimeter.

Answer 1

`\qquad \textit{Heron's area formula} \\\\ A=√(s(s-d)(s-e)(s-f))\qquad \begin{cases} s=(d+e+f)/(2)\\[-0.5em] \hrulefill\\ d = 98\\ e = 35\\ f = 97\\ s=(98+35+97)/(2)\\ \qquad 115 \end{cases} \\\\\\ A=√(115(115-98)(115-35)(115-97)) \\\\\\ A=√(115(17)(80)(18)) \implies A=√(2815200)\implies A\approx 1677.9~cm^2`