Question

Question
Find the surface area of the regular pyramid.

Answer 1

1240.4 mm²

Explanation:

The surface area of a pyramid = Area of the all sides + Area of base

Each side is a triangle.

With a regular pentagonal pyramid, the area of each triangle is

A = 1/2 x base x slant height

For the 5 triangles,

A = 5 x 1/2 x base x slant height = 1/2 x 5 x slant height

Substitute values,

A = 5 x 1/2 x 16mm x 20mm = 800 mm²

Area of base = 440.4 mm²

Surface area of a pyramid = 800 + 440.4 mm² = 1240.4 mm²

Answer 2

Surface area:

• The sum of all the sides to a figure.

Given that the area of the base is 440.4, all we would need to find out is the sum of all the areas of the triangles surrounding it.

Formula for area of a triangle:

A = BH x 1/2

Where 'B' represents the base, 'H' stands for the height, and 1/2 simply means to divide the product of those two lengths(base and height) by 2.

Plug in what we know:-

A = BH x 1/2

A = 16(20) x 1/2

A = 320 x 1/2

A = 320/2

A = 160 mm is the area of one triangle, but we want to know the area of all 5 triangles, so;

160(5)

= 800 mm is the area of all the triangles.

Now add the base area to the area of all the triangles.

440.4 + 800

= 1,240.4 mm.

Therefore the surface area of this pyramid is 1,240.4 mm.