# Base of house

Calculate the volume of the bases of a square house, if the base depth is 1.2 m, the width is 40 cm and their outer circumference is 40.7 m.

Correct result:

V =  18.768 m3

#### Solution:

$h=1.2 \ \text{m} \ \\ s=40 \ cm \rightarrow m=40 / 100 \ m=0.4 \ m \ \\ o=40.7 \ \text{m} \ \\ \ \\ a=o/4=40.7/4=\dfrac{ 407 }{ 40 }=10.175 \ \text{m} \ \\ b=a - 2 \cdot \ s=10.175 - 2 \cdot \ 0.4=\dfrac{ 75 }{ 8 }=9.375 \ \text{m} \ \\ \ \\ S_{1}=a^2=10.175^2 \doteq 103.5306 \ \text{m}^2 \ \\ S_{2}=b^2=9.375^2 \doteq \dfrac{ 5625 }{ 64 } \doteq 87.8906 \ \text{m}^2 \ \\ \ \\ S=S_{1}-S_{2}=103.5306-87.8906=\dfrac{ 391 }{ 25 }=15.64 \ \text{m}^2 \ \\ V=S \cdot \ h=15.64 \cdot \ 1.2=\dfrac{ 2346 }{ 125 }=18.768 \ \text{m}^3$

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