Quadrilateral pyramid

Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture.

Correct answer:

h =  9.1652 cm
S =  224 cm²

Step-by-step explanation:

$$\begin{gathered} a=8\text{ cm } \\ w=10\text{ cm } \\ {w}^2=(a\mathrm{/}2{)}^2+h^2 \\ h=\sqrt{w^2-(a\mathrm{/}2{)}^2}=\sqrt{10^2-(8\mathrm{/}2{)}^2}=2\sqrt{21}=9.1652\text{ cm} \end{gathered}$$

$$\begin{gathered} S_1=a^2=8^2=64{\text{cm}}^2 \\ {S}_2={\displaystyle \frac{a\cdot w}{2}}={\displaystyle \frac{8\cdot 10}{2}}=40{\text{cm}}^2 \\ S=S_1+4\cdot S_2=64+4\cdot 40=224{\text{cm}}^2 \end{gathered}$$

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