Quadrilateral 40551

Find the volume and surface area of ​​a regular quadrilateral pyramid ABCDV if its leading edge has a length a = 10 cm and a body height h = 12 cm.

Correct answer:

V =  400 cm³
S =  360 cm²

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ h=12\text{cm} \\ {S}_1=a^2=10^2=100{\text{cm}}^2 \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 100\cdot 12=400{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} h_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{12^2+(10/2{)}^2}=13\text{cm} \\ {S}_2=\frac{1}{2}\cdot a\cdot h_2=\frac{1}{2}\cdot 10\cdot 13=65{\text{cm}}^2 \\ S=S_1+4\cdot S_2=100+4\cdot 65=360{\text{cm}}^2 \end{gathered}$$

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