House plot trapezoid

The Douglases will build a house. Their plot is a trapezoid with bases 42 m and 18 m long, and the distance between the bases is 23 m. According to the project, the house will have a built-up area of 146 m². How many square meters of land will remain undeveloped?

Final Answer:

S₂ =  544 m²

Step-by-step explanation:

$$\begin{gathered} a=42\text{m} \\ c=18\text{m} \\ v=23\text{m} \\ {S}_1=146{\text{m}}^2 \\ S=\frac{a+c}{2}\cdot v=\frac{42+18}{2}\cdot 23=690{\text{m}}^2 \\ {S}_2=S-S_1=690-146=544{\text{m}}^2 \end{gathered}$$

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