Exercise 55 Page 67

We have been given the following figure for the playpen.

In order to calculate the cost of the dog grass, first thing we need to do is to find the area of the playpen. As you can see the playpen consist of one rectangle and two congruent right triangles. Let's find the rectangle. To find the area of a rectangle with a base b and a height h, we use the following formula. A= b hOur rectangle has a base 3 ft and a height 6 ft. Let's substitute these values into the formula to find the area.

A_R=bh

SubstituteII

b= 3, h= 6

A_R= 3* 6

Multiply

Multiply

A_R=18

The area of the rectangle is 18 ft^2. Next, we will find the area of one of the triangles A_T using the following formula since the triangles are right triangles. A=1/2 b h=b h/2 The triangles have a base 3 ft and a height 1 ft. Again, we will substitute these values into the formula to find the area.

A_T=bh/2

SubstituteII

b= 3, h= 6

A_R=3* 1/2

Multiply

Multiply

A_R=3/2

CalcQuot

Calculate quotient

A_R=1.5

The area of the one of the triangles is 1.5 ft^2. Now, we will add the areas of the rectangle and the triangles to find the area of the pen A_P.

A_P=A_T+A_R+A_T

SubstituteValues

Substitute values

A_P=1.5+18+1.5

AddTerms

Add terms

A_P=21

As a result, the area of the pen is 21 ft^2. Finally, we can find the total cost of the dog grass C by multiplying the cost of it per square foot by the area. C=21(1.70)=35.7 Thus, the cost is $35.70.