Question 1: Find the perimeter of the base
- Definition of Perimeter: it is all the side lengths of the shape added up
- What do we know
-the pentagon is a regular pentagon meaning all its side lengths
are equal since all the sides have one tick mark which says all
the side lengths are equal
2. Solve:
Perimeter: 6 + 6 + 6 + 6 + 6 = 30cm
Question 2: Find the height of the prism
⇒ distance between the base pentagon and the top pentagon
⇒ Height is 6 cm
Question 3: Find the Lateral Area
- Definition of Lateral Area: it is only the area of the non-base faces
⇒ the non-base faces are the squares on the side of the figure
⇒ there are 5 squares
⇒ Lateral Area = 5 * (Area of Square) = 5 * (6 * 6) = 180 square cm
Question 4: Find the area of the base
The formula for the pentagon's area ⇒ [tex]\frac{5}{2}*s*a[/tex]
- s --> length of the sides of the pentagon --> 6cm
- a --> apothem length --> 4.1 cm
*apothem is the distance from the center of the pentagon to any
one of the sides
Area = [tex]\frac{5}{2} *6*4.1 = 15 * 4.1 =[/tex] 61.5 square centimeters
Question 5: Find the surface area
- Definition of Surface Area: all the areas of different sides added up
Surface Area = 2 * (Area of Base) + (Lateral Area)
= 2 *61.5 + 180 = 123 + 180 = 303 square centimeters
Hope that helps!
