Exercise 3 Page 875

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 Will calculate the perimeter of the base P, the area of the base B, and the surface area of the solid S one at a time.

Perimeter of the Base

The given solid is a triangular prism with height 18 feet. The base is an isosceles triangle with height 8 feet and base 14 feet.

The height of the triangle divides it into two right triangles. Also, the height bisects the base of the triangle. Therefore, we have two congruent right triangles with base length 14÷ 2= 7 feet and height 8 feet.

By finding the hypotenuse c, we will be able to find the perimeter of the base of the prism. Let's use the Pythagorean Theorem to find c.

c^2=a^2+b^2

SubstituteII

a= 8, b= 7

c^2= 8^2+ 7^2

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Solve for c

CalcPow

Calculate power

c^2=64+49

AddTerms

Add terms

c^2=113

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c=sqrt(113)

The length of the congruent sides of the base of the prism is sqrt(113) feet.

We now know the lengths of the three sides of the base. Let's add them to find the perimeter of the base. P&= 14+ sqrt(113)+ sqrt(113) P&= 14+2sqrt(113)