Area of the Base = 6 * side^2 / 4 * tan (180/6)
Area of the Base = 6 * 16 / 4 * 0.57735
Area of the Base = 96 / 2.3094
Area of the Base = 41.5692387633
Area of 1 Face = 2 * 6 = 12
Area of 6 Faces = 72
Total Area = 41.5692387633 + 72
Total Area = 113.5692387633
Answer:
m∠EGF = 65° and m∠CGF = 115°
Step-by-step explanation:
Given;
∠EFG = 50°
EF = FG
Solution,
In ΔEFG m∠EFG = 50° and EF = FG.
Since triangle is an isosceles triangle hence their base angles are always equal.
∴
Let the measure of ∠EGF be x.
∴ 
Now by angle Sum property which states "The sum of all the angles of a triangle is 180°."
m∠EFG + m∠FEG + ∠EGF = 180
Hence
m∠EGF = 65°
Also 'The sum of angles that are formed on a straight line is equal to 180°."
m∠EGF + m∠CGF = 180°
65° + m∠CGF = 180°
m∠CGF = 180° - 65° = 115°
Hence m∠EGF = 65° m∠CGF = 115°
Using the Euler's formula, the number of segments in the pentagonal prism is: 15.
<h3>What is the Euler's Formula?</h3>
The Euler's formula is given as, F + V = E + 2, where:
- F = number of faces (number of regions)
- V = vertices
- E = number of edges (number of segments).
Given that the pentagonal prism has the following dimensions:
- F = 7
- V = 10
- E = number of segments = ?
Plug in the values into the Euler's formula, F + V = E + 2:
7 + 10 = E + 2
17 - 2 = E
E = 15
Therefore, using the Euler's formula, the number of segments in the pentagonal prism is: 15.
Learn more about the Euler's formula on:
brainly.com/question/1178790
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