Chapter 11, Problem 12MCQ

To determine

To calculate: The amount of fabric would be necessary to make a curtain for the doorway.

Answer to Problem 12MCQ

The fabric necessary to make a curtain for the doorway is $19.833{\text{ft}}^{\text{2}}$ .

Explanation of Solution

Given information:

The most predominant shape in Incan architecture is the trapezoid. The doorway given is $3\text{feet}$ wide at the top and $4\text{ft}$ wide at the bottom. A person who is $5\text{ft}8\text{in}$ tall can barely pass through the doorway.

Concept Used:

The area of the trapezoidal shape whose parallel sides are $a,b$ and the distance between the parallel sides is $h$

  

Calculation:

As per the given question

The width of the top of trapezoid doorway is $a=3\text{ft}$

The width of the bottom of trapeziod doorway is $b=4\text{ft}$

A person who is $5\text{ft}8\text{in}$ tall can barely paas through this doorway means it is the height of doorway or distance between the top and bottom side.

  $h=5\text{ft}\text{8 in}$

  $\begin{array}{l}1\text{ft}=12\text{in}\\ \text{Then 1 in}=\text{ 0}\text{.6667}\text{ft}\end{array}$

  $h=5.6667\text{ft}$

The fabric necessary for this doorway means we have to find the area of this doorway,

Area of trapezoid shape is

  

Now,

  

Area of the doorway is $19.833{\text{ft}}^{\text{2}}$ .

Conclusion:

The fabric necessary to make a curtain for the doorway is $19.833{\text{ft}}^{\text{2}}$ .