The slant height of a regular pentagonal pyramid is 6 cm, and the length of each side of the base is 3 cm. Find the lateral area.
This site explains how to do this.
http://www.mathsisfun.com/geometry/pyramids.html
LA = PHs/2 = (5*3)*6 / 2 = 45cm^2.
LA = Lateral Area.
P = Perimeter.
Hs = slant Height.
To find the lateral area of a regular pentagonal pyramid, we need to know the slant height and the side length of the base.
The formula to find the lateral area of a regular pentagonal pyramid is:
Lateral Area = (perimeter of the base * slant height) / 2
Step 1: Find the perimeter of the base:
Since the base of the pyramid is a regular pentagon, it has 5 equal sides.
Perimeter of the base = 5 * length of each side
Perimeter of the base = 5 * 3 cm
Perimeter of the base = 15 cm
Step 2: Substitute the values into the formula:
Lateral Area = (15 cm * 6 cm) / 2
Lateral Area = 90 cm^2 / 2
Lateral Area = 45 cm^2
Therefore, the lateral area of the regular pentagonal pyramid is 45 cm^2.
To find the lateral area of the regular pentagonal pyramid, we need to know the slant height and the length of each side of the base.
In this case, we have the slant height (l) = 6 cm and the length of each side of the base (s) = 3 cm.
To calculate the lateral area, we use the formula:
Lateral area = (1/2) × perimeter of the base × slant height
The perimeter of the base is the sum of all the sides of the base. The regular pentagon has five equal sides, so the perimeter is:
Perimeter of the base = 5 × length of each side = 5 × 3 cm = 15 cm
Substituting the values into the formula, we have:
Lateral area = (1/2) × 15 cm × 6 cm
= 7.5 cm × 6 cm
= 45 cm^2
Therefore, the lateral area of the regular pentagonal pyramid is 45 cm^2.