Question

Find the surface area of a regualar pyramid that is a pentagonal pyramid with the area of a base is is 440.4mm and a height of 20mm and a slant of 20mm and the side base of 16mm

Answer 1

Answer:

1240.4 mm²

Step-by-step 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

$A = \frac{1}{2}\times\text{base}\times\text{slant height}$

For the 5 triangles,

$A = 5\times\frac{1}{2}\times\text{base}\times\text{slant height} = \frac{1}{2}\times5\times\text{base}\times\text{slant height}$

Substituting given values,

$A = 5\times\frac{1}{2}\times16\ \text{mm}\times20\ \text{mm} = 800 \text{mm}^2$

Area of base = 440.4 mm²

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