Square triangle area

The area of the ABCD square in the picture is 36 cm². Points E and F are the centers of the square BC and CD sides. What is the area of the triangle AEF in cm²?

Final Answer:

S =  13.5 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=36{\text{cm}}^2 \\ {S}_1=a^2 \\ a=\sqrt{S_1}=\sqrt{36}=6\text{cm} \\ {b}^2=(a/2{)}^2+(a/2{)}^2 \\ b=\sqrt{(a/2{)}^2+(a/2{)}^2}=\sqrt{(6/2{)}^2+(6/2{)}^2}=3\sqrt{2}\text{cm}\doteq 4.2426\text{cm} \\ {S}_2=\frac{a/2\cdot a}{2}=\frac{6/2\cdot 6}{2}=9{\text{cm}}^2 \\ {S}_3=\frac{a/2\cdot a/2}{2}=\frac{6/2\cdot 6/2}{2}=\frac{9}{2}=4.5{\text{cm}}^2 \\ S=S_1-2\cdot S_2-S_3=36-2\cdot 9-\frac{9}{2}=\frac{27}{2}{\text{cm}}^2=13.5{\text{cm}}^2 \end{gathered}$$

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