Chapter 1.6, Problem 9CYU

To determine

To calculate which shape will take the most fabric

Answer to Problem 9CYU

Circle banner will take the most/ almost all the cloth

Explanation of Solution

Given information:

Total fabric Vanesa has is 20 square feet.

Banner shape options:

1. A square with side length of 4feet
2. Rectangle with length 4 feet and width 3.5feet
3. A circle with radius 2.5 feet
4. Right triangle with legs of 5 feet

Formula used:

  Area of square,

  $area=sid{e}^2$

  Area of rectangle,

  $area=lw$

  Area of circle,

  $area=\pi r^2$

  Area of triangle,

  $area=\frac{1}{2}bh$

Calculation:

For the area of square banner, substituting the value,

  $area=4^2$

On solving,

  $area=16$

Hence, cloth required for square banner is 16 feet square.

For the area of rectangle banner, substituting the value,

  $area=4\times 3.5$

On solving,

  $area=14$

Hence, cloth required for rectangle banner is 14 feet square.

For the area of circle banner, substituting the value,

  $area=3.14\times {(2.5)}^2$

On solving,

  $area=19.625$

Hence, cloth required for circle banner is 19.625 feet square.

For the area of triangle banner, substituting the value,

  $area=\frac{1}{2}\times 5\times 5$

On solving,

  $area=12.5$

Hence, cloth required for triangle banner is 12.5 feet square.

Therefore, a circle banner will take the most/ almost all the cloth