Quadrilateral 41061

A quadrilateral pyramid has a square base 4 cm long, the height of the pyramid 5 cm, and the height of the wall 5.4 cm. Find the surface and volume of a quadrilateral pyramid.

Correct answer:

S =  59.2 cm²
V =  26.6667 cm³

Step-by-step explanation:

$$\begin{gathered} a=4\text{cm} \\ h=5\text{cm} \\ s=5.4\text{cm} \\ {S}_1=\frac{a\cdot s}{2}=\frac{4\cdot 5.4}{2}=\frac{54}{5}=10.8{\text{cm}}^2 \\ {S}_2=a^2=4^2=16{\text{cm}}^2 \\ S=S_2+4\cdot S_1=16+4\cdot 10.8=\frac{296}{5}=59.2=59.2{\text{cm}}^2 \\ \text{ Verifying Solution: } \\ {s}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{5^2+(4/2{)}^2}=\sqrt{29}\text{cm}\doteq 5.3852\text{cm} \\ {s}_2=s \end{gathered}$$

$V=\frac{1}{3}\cdot S_2\cdot h=\frac{1}{3}\cdot 16\cdot 5=26.6667{\text{cm}}^3$

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