Quadrilateral 21523

Calculate the surface area and volume of a regular quadrilateral pyramid if the edge of the lower base is 18 cm and the edge of the upper base is 15 cm. The wall height is 9 cm.

Correct answer:

V =  2422.6347 cm³
S =  1143 cm²

Step-by-step explanation:

$$\begin{gathered} a=18\text{cm} \\ b=15\text{cm} \\ s=9\text{cm} \\ x=(a-b)/2=(18-15)/2=\frac{3}{2}=1.5\text{cm} \\ h=\sqrt{s^2-x^2}=\sqrt{9^2-1.5^2}\doteq 8.8741\text{cm} \\ {S}_1=a^2=18^2=324{\text{cm}}^2 \\ {S}_2=b^2=15^2=225{\text{cm}}^2 \\ V=\frac{h}{3}\cdot (S_1+\sqrt{S_1\cdot S_2}+S_2)=\frac{8.8741}{3}\cdot (324+\sqrt{324\cdot 225}+225)=2422.6347{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_3=(a+b)\cdot s/2=(18+15)\cdot 9/2=\frac{297}{2}=148.5{\text{cm}}^2 \\ S=S_1+S_2+4\cdot S_3=324+225+4\cdot 148.5=1143{\text{cm}}^2 \end{gathered}$$

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