Exercise 26 Page 626

We are given a prism and want to find its surface area.

To calculate the surface area of a prism, we can use the known formula where P is the perimeter of the base, h is the height, and B is the area of the base. S=Ph+2B We are given the lengths of all the base's sides. Let's add them to find the perimeter of the base. P=5+5+5=15cm Note that the base is a equilateral triangle, so we can calculate its area using the formula for area of a triangle.

B=1/2bh

SubstituteII

b= 5, h= 4.3

B=1/2( 5)( 4.3)

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Simplify right-hand side

MoveRightFacToNumOne

1/b* a = a/b

B=(5)(4.3)/2

Multiply

Multiply

B=21.5/2

CalcQuot

Calculate quotient

B=10.75

The area of the base is 10.75m^2. Now we have enough information to find the surface area of the prism. Let's substitute P with 15, h with 14, and B with 10.75 into the formula.

S=Ph+2B

SubstituteValues

Substitute values

S=( 15)( 14)+2( 10.75)

▼

Simplify right-hand side

Multiply

Multiply

S=210+21.5

AddTerms

Add terms

S=231.5

The surface area of the prism is 231.5m^2.