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Big Ideas Math: Modeling Real Life, Grade 6

BI

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

Chapter Review

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Exercise 42 Page 337

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

180.6 square centimeters

Practice makes perfect

We want to calculate the surface area of a square pyramid. Let's see the given measurements of the 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 the square and triangles. Let's calculate the area of each polygon separately, starting with the square.

A=s^2

s= 7

A= 7^2

Calculate power

A=49

The area of the base that is a square is 49 square centimeters. Now let's take a look at the triangles. Note that 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=1/2b* h

b= 7, h= 9.4

A=1/2 ( 7)( 9.4)

Multiply

A=32.9

We found that the area of one triangle is 32.9 square centimeters. Since the triangles are congruent, that means that the area of every triangle is 32.9 square centimeters. Now we have all the information that we need to find the total surface area of the square pyramid! Total Surface Area 49+ 32.9+ 32.9+ 32.9+ 32.9=180.6cm^2 The total surface area of the square pyramid is 180.6 square centimeters.

Subchapter links

1 Areas of Parallelograms p.333

2 Areas of Triangles p.334

3 Areas of Trapezoids and Kites p.335

4 Three-Dimensional Figures p.336

5 Surface Areas of Prisms p.336

6 Surface Areas of Pyramids p.337

7 Volumes of Rectangular Prisms p.337