Chapter 11.9, Problem 5CYU

a.

To determine

To calculate the area of the walkway.

Answer to Problem 5CYU

  $58$ square feet.

Explanation of Solution

Given information:

Figure consists for a rectangle with length $l=6$ feet and breath $b=4$ feet.

It also consists of a trapezoid with parallel sides $a=13$ feet and $b=4$ feet and a height $h=4$ feet.

Formula used:

Area of rectangle $a=l\times b$ . Where ‘l’ is the length and ‘b’ is the breath.

Area of circle $A=\frac{a+b}{2}\times h$ where ‘a’ and ‘b’ are the parallel sides and ‘h’ is the height.

Calculation:

Calculate the area of the rectangle and trapezoid. On adding the two, the area of the figure shall be derived.

  $a=l\times b$

Formula of rectangle

  $=6\times 4$

Multiply the length and breadth

  $=24$ square feet.

Next, calculate area of the trapezoid.

  $A=\frac{a+b}{2}\times h$

Formula of trapezoid.

  $=\frac{13+4}{2}\times 4$

Simplify the expression

  $=17\times 2$

On simplification

  $=34$ square feet.

Adding the two areas would give the area of the figure.

  $=34+24$

  $=58$ square feet.

b.

To determine

To calculate the number of brick cases needed to cover the walkway its total cost.

Answer to Problem 5CYU

10 cases of bricks and total cost of $\$250$ .

Explanation of Solution

Given information:

One case of bricks cost $25 and covers 6 square feet.

From sub-part a., total area of the walkway $=58$ square feet

Total area of the walkway $=58$ square feet

Each brick case covers 6 square feet.

Hence, number of brick cases need $=\frac{58}{6}$

  $=9.66$ cases.

Since this is in a decimal, round this to the upper limit.

Hence it becomes $=10$ cases.

Cost for the same shall be the product of the cost per case, multiplied by the total cases required.

  $=\$25\times 10$

  $=\$250$ This is the total cost.