Given
The unit of length is cm.
Figure not drawn to scale.
Find
Solution
\(
\begin{array}{l}
A_{Green}=A_{\triangle{ABC}}-(A_{\triangle{A}}+A_{\triangle{B}}+A_{\triangle{C}}) \\\\
\text{Assume}\ \angle{CAB} = 90° \\
\overline{CA}^2 + \overline{AB}^2 = \overline{BC}^2 \\
(15\ cm)^2 + (20\ cm)^2 = (25\ cm)^2 \\
625\ cm^2 = 625\ cm^2\ \text{true.} \\\\
A_{\triangle\ ABC} = \frac{[AB] \cdot [AC]}{2} = 150\ cm^2 \\
A_{\triangle{A}} = \frac{(5\ cm)^2}{2} = 12,5\ cm^2 \\
A_{\triangle{B}} = \frac{(5\ cm)^2}{2} \cdot sin(\angle{ABC}) = 12,5\ cm^2 \cdot \frac{[AC]}{[BC]} = 7,5\ cm^2 \\
A_{\triangle{C}} = \frac{(5\ cm)^2}{2} \cdot sin(\angle{ACB}) = 12,5\ cm^2 \cdot \frac{[AB]}{[BC]} = 10\ cm^2 \\
A_{Green} = 150\ cm^2 – (12,5\ cm^2 + 7,5\ cm^2 + 10\ cm^2) = 120\ cm^2
\end{array}
\)
Answer