Parcel

The parcel is rectangular, a trapezoid with bases of 12 m and 10 m and a height of 8 m. On the parcel was a built object with a footprint of an isosceles triangle, with a side of 4 m and a height of three-quarters of a meter. What is the area of the unbuilt parcel?

Final Answer:

S =  86.5 m²

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ c=10\text{m} \\ h=8\text{m} \\ x=4\text{m} \\ v=3/4=\frac{3}{4}=0.75\text{m} \\ {S}_1=\frac{a+c}{2}\cdot h=\frac{12+10}{2}\cdot 8=88{\text{m}}^2 \\ {S}_2=\frac{x\cdot v}{2}=\frac{4\cdot 0.75}{2}=\frac{3}{2}=1.5{\text{m}}^2 \\ S=S_1-S_2=88-1.5=86.5{\text{m}}^2 \end{gathered}$$

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