Surface Area of Pyramids

Surface Area of Pyramids

The Shapes That Make Up A Pyramid

This clip shows you that shapes and what they are referenced as.

Surface Area of Pyramids

• A pyramid is composed of a base and triangular faces.

• The pyramid is named by the shape of the base.

• EX: Square pyramid, Rectangular pyramid, Triangular Pyramid, etc.

• The lateral height, also called the slant height, is the height of the triangular face.

Multiple Select

Mark all that are correct.

• L is the lateral face

• The shape is a Rectangular Pyramid

• a is the lateral face

• b is the base

• L is the lateral height

Multiple Choice

Find the area of 1 square base.

• 14 mm²

• 7 mm²

• 42 mm²

• 49 mm²

Multiple Choice

How many bases do we have?

• 1

• 2

• 3

• 4

Multiple Choice

What is the total area of the base if we only have 1 base?

• 14 mm²

• 7 mm²

• 42 mm²

• 49 mm²

Multiple Choice

Find the area of 1 of the lateral faces?

• 42 mm²

• 7 mm²

• 21 mm²

• 6 mm²

Multiple Choice

How many lateral faces do we have?

• 1

• 2

• 3

• 4

Multiple Choice

What is the total area of the lateral faces if we have 4?

• 84 mm²

• 21 mm²

• 42 mm²

• 63 mm²

Multiple Choice

What is the total area of the square pyramid?

*Remember: Add the total areas of each shape*

• 84 mm²

• 123 mm²

• 132 mm²

• 133 mm²

SA Of a Pyramid

• Shape 1: Base

• Find the area of the base depending on the shape

• Ex:  $\left(l\times w\right)$  for a square or rectangle.

• Shape 2: Lateral Face

• This will be the triangle

•  $Area\ =\ \frac{b\times\left(lateral\ height\right)}{2}$  

• Finally, add the areas together.

Multiple Choice

^{_{Find the Surface Area}}

• 15m²
• 16m²
• 18m²
• 20m²

Rectangular Pyramid

• This process is similar, but not all triangles are the same.

• The net shown to the right prove that the triangles parallel from each other are the same. They are across from each other.

Multiple Choice

Find the area of the base

• 12 ft²

• 18 ft^2

• 24 ft²

• 10 ft²

Multiple Choice

Find the area of 1 of the lateral faces that have a slant height of 5 ft.

• 10 ft²

• 15 ft^2

• 12 ft²

• 24 ft²

Multiple Choice

Find the area of 1 of the lateral faces that have a slant height of 4 ft.

• 10 ft²

• 15 ft^2

• 12 ft²

• 24 ft²

Multiple Choice

Find the total area of the rectangular pyramid.

• 44 ft²

• 55 ft^2

• 66 ft²

• 68 ft²

Fill in the Blank

What is the lateral surface area of the pyramid in square feet? (Do not include units in your answer, just the number)

Multiple Choice

What is the surface area of this triangular pyramid?

• 198.9 sq. inches

• 205.6 sq. inches

• 187.9 sq. inches

• 210.6 sq. inches

Multiple Choice

Find the lateral surface area of this triangular pyramid.

These are equilateral triangles, so each triangle is the same is the middle triangle.

• 27 ft²

• 81 ft²

• 54 ft²

• 108 ft²

Multiple Choice

Find the total surface area of this triangular pyramid.

* You already found the lateral face area. Just find the base and add it.

• 27 ft²

• 81 ft²

• 54 ft²

• 108 ft²