Quadrilateral 6332

The regular quadrilateral pyramid is 2 m high. The height of the sidewall is 2.8 m. What are the dimensions of the base? Calculate the surface area and volume of the pyramid.

Correct answer:

a =  3.9192 m
S =  37.3074 m²
V =  10.24 m³

Step-by-step explanation:

$$\begin{gathered} h_1=2\text{m} \\ {h}_2=2.8\text{m} \\ (a/2{)}^2+h_1^2=h_2^2 \\ a=2\cdot \sqrt{h_2^2-h_1^2}=2\cdot \sqrt{2.8^2-2^2}=3.9192\text{m} \end{gathered}$$

$$\begin{gathered} S_1=a^2=3.9192^2=\frac{384}{25}=15.36{\text{m}}^2 \\ {S}_2=a\cdot h_2/2=3.9192\cdot 2.8/2\doteq 5.4869{\text{m}}^2 \\ S=S_1+4\cdot S_2=15.36+4\cdot 5.4869=37.3074{\text{m}}^2 \end{gathered}$$

$V=\frac{1}{3}\cdot S_1\cdot h_1=\frac{1}{3}\cdot 15.36\cdot 2=\frac{256}{25}{\text{m}}^3=10.24{\text{m}}^3$

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