Exercise 43 Page 337

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

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

Substitute

s= 5

A= 5^2

CalcPow

Calculate power

A=25

The area of the base that is a square is 25 square inches. 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

SubstituteII

b= 5, h= 5.5

A=1/2 ( 5)( 5.5)

Multiply

Multiply

A=13.75

We found that the area of one triangle is 13.75 square inches. Since the triangles are congruent, that means that the area of every triangle is 13.75 square inches. Now we have all the information that we need to find the total surface area of the square pyramid! Total Surface Area 25+ 13.75+ 13.75+ 13.75+ 13.75=80in.^2 The total surface area of the square pyramid is 80 square inches.