The tent

Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m.

Correct result:

S =  15 m2

Solution:

a=3 m h=2 m  h2=h2+(a/2)2=22+(3/2)2=52=2.5 m  S1=a⋅ h2/2=3⋅ 2.5/2=154=3.75 m2  S=4⋅ S1=4⋅ 3.75=15 m2a=3 \ \text{m} \ \\ h=2 \ \text{m} \ \\ \ \\ h_{2}=\sqrt{ h^2 + (a/2)^2 }=\sqrt{ 2^2 + (3/2)^2 }=\dfrac{ 5 }{ 2 }=2.5 \ \text{m} \ \\ \ \\ S_{1}=a \cdot \ h_{2}/2=3 \cdot \ 2.5/2=\dfrac{ 15 }{ 4 }=3.75 \ \text{m}^2 \ \\ \ \\ S=4 \cdot \ S_{1}=4 \cdot \ 3.75=15 \ \text{m}^2

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