Pyramid complete

A regular quadrilateral pyramid is given: a = 27 mm, w = 21 mm (wall height). Calculate the height, volume, and surface area of the pyramid.

Final Answer:

S =  18.6 cm²
V =  3.9 cm³

Step-by-step explanation:

$$\begin{gathered} a=27\text{mm}\to \text{cm}=27:10\text{cm}=2.7\text{cm} \\ w=21\text{mm}\to \text{cm}=21:10\text{cm}=2.1\text{cm} \\ {S}_1=a^2=2.7^2=\frac{729}{100}=7.29{\text{cm}}^2 \\ {w}^2=h^2+(a/2{)}^2 \\ h=\sqrt{w^2-(a/2{)}^2}=\sqrt{2.1^2-(2.7/2{)}^2}\doteq 1.6086\text{cm} \\ {S}_2=a\cdot w/2=2.7\cdot 2.1/2=\frac{567}{200}=2.835{\text{cm}}^2 \\ S=S_1+4\cdot S_2=7.29+4\cdot 2.835=18.6{\text{cm}}^2 \end{gathered}$$

$V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 7.29\cdot 1.6086=3.9{\text{cm}}^3$

Try another example