Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Review
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Exercise 17 Page 753

576 m^2

Practice makes perfect

The given solid is a pyramid.

To calculate the surface area of a pyramid, we can use the known formula where P is the perimeter of the base, l is the slant height, and B is the area of the base. S=1/2Pl+B The base of the pyramid is a square with the side length of 16m. Let's calculate its perimeter! P=4s ⇒ P=4( 16)=64m The area of the square equals the squared length of the side. B=s^2 ⇒ B= 16^2=256m^2 We are also given that the slant height l is 10m. Let's substitute all of these values into the formula for the surface area and calculate it.
S=1/2Pl+B
S=1/2( 64)( 10)+ 256
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Simplify right-hand side
S=1/2(640)+256
S=640/2+256
S=320+256
S=576
The surface area of the pyramid is 576 m^2.