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Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

6. Surface Areas of Pyramids

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Exercise 16 Page 323

Use a net to find the surface area of the square pyramid.

172.8 square yards

Practice makes perfect

We want to calculate the surface area of a square pyramid. Let's see the given pyramid.

We can use a net to calculate the surface area of the pyramid. Let's see the net!

The net is made up of a square and four triangles. Let's calculate the area of each polygon separately, starting with the square.

A=s^2

s= 6

A= 6^2

Calculate power

A=36

The area of the square base is 36 square yards. Now let's take a look at the triangles. Notice that the sides of the pyramid are congruent triangles. This means that they have the same area. Let's substitute the measures of the sides into the formula for the area of a triangle!

A=1/2bh

b= 6, h= 11.4

A=1/2* 6* 11.4

Multiply

A=34.2

We found that the area of one triangle is 34.2 square yards. Since the triangles are congruent, the area of each triangle is 34.2 square yards. Now we have all the information that we need to find the total surface area of the square pyramid! Total Surface Area 36+ 34.2+ 34.2+ 34.2+ 34.2=172.8yd^2 The total surface area of the square pyramid is 172.8 square yards.

Subchapter links

Try It p.320-321

Self-Assessment for Concepts & Skills p.321

Self-Assessment for Problem Solving p.322

Review & Refresh p.323

Concepts, Skills, & Problem Solving p.323-324