Pyramid

 

A pyramid is a three dimensional shape made up of a base and triangular faces that meet up at the vertex, V, which is also called the apex of the pyramid.

pyramid

Surface area of a pyramid

The surface area is composed by two parts: the area of the base and the lateral area.

Area of the base

It depends on the shape, you have to use the correct formula if the base is composed by a triangle, square, ecc.

Lateral surface

Since the side faces are triangles and the formula for the area of a triangle is

area triangolo

All you need to do is multiply the area of the base by the slant lenght and divide by two

area laterale piramide

Inverse formulae:

area laterale piramide inv2

area laterale piramide inv1

Volume of the pyramid

volume piramide.png

Inverse formulae:

volume piramide inv2

volume piramide inv1

Exercises

  1. A pyramid has slant lenght 10 cm long. The base is a square with a side of 7 cm. Calculate the total surface area. Solution
  2. A pyramid has a slant lenght 125 cm long. The lateral surface is 450 dm2. Calculate the perimeter of the base. Solution
  3. A pyramid has a volume of 1840 cm3. The base is a square that has an area of 1.84 cm2. Calculate the height of the pyramid. Solution
  4. The base of a pyramid is a rhombus, that has an area of 37 cm2. Calculate the lateral surface area knowing that the total surface area is 140.5 cm2.
  5. The base of a pyramid is an isosceles triangle ABC with AB = 10 cm and the height CH = 12 cm. The height of the pyramid is 15 cm. Calculate the volume of the pyramid.

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