Quadrangle ACEG

The figure shows two rectangles ABCD and DEFG, with |DE| = 3 cm, |AD| = 6 cm, |DG| = 5 cm, and |CD| = 10 cm. Calculate the area of quadrilateral ACEG.

Figure description: the two rectangles share vertex D. Rectangle ABCD has sides twice as long as those of DEFG. All sides are either parallel or perpendicular to each other.

Final Answer:

S =  67.5 cm²

Step-by-step explanation:

$$\begin{gathered} a=3\text{cm} \\ A=6\text{cm} \\ b=5\text{cm} \\ B=10\text{cm} \\ {S}_1=\frac{A\cdot B}{2}=\frac{6\cdot 10}{2}=30{\text{cm}}^2 \\ {S}_2=\frac{A\cdot b}{2}=\frac{6\cdot 5}{2}=15{\text{cm}}^2 \\ {S}_3=\frac{a\cdot b}{2}=\frac{3\cdot 5}{2}=\frac{15}{2}=7.5{\text{cm}}^2 \\ {S}_4=\frac{a\cdot B}{2}=\frac{3\cdot 10}{2}=15{\text{cm}}^2 \\ S=S_1+S_2+S_3+S_4=30+15+7.5+15=67.5{\text{cm}}^2 \end{gathered}$$

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