Chapter 11.9, Problem 17PPS

To determine

To calculate the shuffleboard court.

Answer to Problem 17PPS

  $35.25$ square feet.

Explanation of Solution

Given information:

The shuffleboard court consists of a triangle and a trapezoid.

Triangle has a base of $b=6$ feet and height $h_1=9$ feet.

Trapezoid has parallel lengths of $l_1=6-1$

  $=5$ feet (since 12 inches is equal to 1 feet) and $l_2=6$ feet. The height of the trapezoid is $h_2=1\frac{1}{2}$

  $=\frac{3}{2}$ feet.

Formula used:

Area of triangle $a=\frac{1}{2}\times b\times h_1$ where ‘b’ is the base and ‘ $h_1$’ is the height.

Area of trapezoid is $t=\frac{l_1+l_2}{2}\times h_2$ where ‘ $l_1$ ’ and ‘ $l_2$ ’ are the parallel sides and ‘ $h_2$ ’ is the height.

Calculation:

Area of the triangle

  $a=\frac{1}{2}\times b\times h_1$

Putting values in the same

  $=\frac{1}{2}\times 6\times 9$

Multiply the expression

  $=27$ square feet

Area of trapezoid.

  $t=\frac{l_1+l_2}{2}\times h_2$

Formula for area of trapezoid.

  $=\frac{5+6}{2}\times \frac{3}{2}$

Putting the values in the formula

  $=\frac{11}{2}\times \frac{3}{2}$

Dividing common terms and simplifying

  $=8.25$ square feet.

Now, add the two areas to get the area of the given figure.

  $=a+t$

Putting values of the two respective areas.

  $=27+8.25$

It becomes

  $=35.25$ square feet.