Square quadrilateral area

The picture shows a square ABCD with the center S and the side 8 cm long. Point E is any point on the CD side other than C and D. Calculate the area of the ASBE quadrilateral in cm².

Final Answer:

S =  16 cm²

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ \Delta ASB \\ {S}_1=\frac{a^2}{4}=\frac{8^2}{4}=16{\text{cm}}^2 \\ \Delta AEB \\ {S}_2=\frac{a\cdot a}{2}=\frac{8\cdot 8}{2}=32{\text{cm}}^2 \\ S=S_2-S_1=32-16=16{\text{cm}}^2 \end{gathered}$$

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