Question

10 POINTS!
Find the lateral area and the surface area of the regular hexagonal pyramid.

Answer 1

Lateral area = 210 cm² , Surface area = 325.5 cm²

Explanation:

lateral area:( (7 x 10) x 6) /2 = 210

surface area = lateral area + base area = 210 + ((7 x 5.5) /2 x 6)

= 210 + 115.5 = 325.5

Answer 2

Lateral area = 210cm², Surface area = 325.5cm²

Explanation:

To find the lateral area and surface area of hexagonal pyramid we work with their respectively formulas.

Given that

Apothem length = 5.5cm

Edge length = 7cm

slant height = 10cm

Number of edges = 6

Formula for Lateral area of hexagonal pyramid = 1/2(perimeter)(slant height)

Perimeter = edge length x number of edges

Perimeter = 7cm x 6 = 42cm

Therefore

Lateral area = 1/2 * 42 * 10

Lateral area = 210cm²

Formula for surface area of hexagonal pyramid = Area of base + lateral area

Where, Area of base = 1/2(apothem length)(perimeter)

Area of base = 1/2 * 5.5 * 42

Area of base = 115.5cm²

Therefore

Surface Area= Area of base + lateral area

Surface Area = 115.5cm² + 210cm²

Surface Area = 325.5cm²

Therefore

Lateral area = 210cm², Surface area = 325.5cm²