Surface Area of Pyramids

SECTION 5.07

After completing this lesson, you will be able to say:

I can represent three-dimensional figures using nets made of rectangles and triangles.

I can use nets to find the surface area of three-dimensional figures.

I can use nets to solve problems about surface area.

Pyramids

What Is a Pyramid?

Pyramid:A polyhedron that contains one base with three or more faces that meet at a point.

Types of Pyramids

Rectangular Pyramid • base is a rectangle.• There are 4 triangular faces

connected at the top point to form the pyramid.

• Opposite triangular faces are congruent.

Types of Pyramids

Square Pyramid• base is a square.• There are 4 triangular faces

connected at the top point to form the pyramid.

• The four triangular faces are congruent.

Types of Pyramids

Triangular Pyramid • base is a triangle.• There are 3 triangular faces

connected at the top point to form the pyramid.

• If any of the sides of the triangle base are congruent, then the faces attached to those sides will be congruent to each other.

Types of Pyramids

Pentagonal Pyramid• base is a pentagon.• There are 5 triangular faces

connected at the top point to form the pyramid.

Types of Pyramids

Hexagonal Pyramid• base is a hexagon.• There are 6 triangular faces

connected at the top point to form the pyramid.

Surface Area of Pyramids

We can use the nets of Pyramids to find the surface area.

Now, let's calculate the area of the square base. Area of the square base:8 in × 8 in = 64 in2

The last part in the calculation is to just determine the sum of all the faces. Total surface area of the pyramid:176 in2 + 64 in2 = 240 in2

Try it

Can you find the surface area of this pyramid?

Check your work

Total surface area:130 cm2 + 163.48 cm2 + 134 cm2 = 427.48 cm2

Now that you completed this lesson, you should be able to say:

I can represent three-dimensional figures using nets made of rectangles and triangles.

I can use nets to find the surface area of three-dimensional figures.

I can use nets to solve problems about surface area.