IXL | Lateral area of prisms and pyramids | 7th grade math

or

A triangular prism is shown below.

Which diagram is a net for the prism?

What is the lateral area of the triangular prism?

square millimeters

ref_doc_title.

or

Learn with an example

question

A triangular pyramid is shown below. Its base is an equilateral triangle with a side length of

5

millimeters

.

Which diagram is a net for the pyramid?

What is the lateral area of the triangular pyramid?

square millimeters

key idea

A net shows all of the faces of a three-dimensional figure.

A triangular pyramid has a triangular base and three triangular lateral faces. Its lateral area is the sum of the areas of the lateral faces.

solution

Four faces make up the triangular pyramid:

one triangular base with a side length of
5
millimeters
three triangular lateral faces, each with a base of
5
millimeters
and a height of
9
millimeters

This is a net for the pyramid. It shows all of the faces and, when folded up, will form the pyramid.

To find the lateral area of the pyramid, add up the areas of the three triangular lateral faces.

All three triangular lateral faces have a base of

5

millimeters

and a height of

9

millimeters

.

Find the area of one of them.

A

=

1

2

b

h

A

=

1

2

(

5

)

(

9

)

A

=

1

2

(

45

)

A

=

22.5

square millimeters

Finally, multiply

22.5

square millimeters

by 3.

3

(

22.5

)

=

67.5

The lateral area of the triangular pyramid is

67.5

square millimeters

.

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Not feeling ready yet? These can help:

FF.3Nets of three-dimensional figures

GG.2Area of rectangles and squares

GG.6Area of triangles