Chapter 11.3, Problem 13PSB

To determine

To Calculate: Area of the trapezoid.

Answer to Problem 13PSB

The area of the trapezoid is $72$ square units.

Explanation of Solution

Given information:

The consecutive sides of an isosceles trapezoid are in the ratio $2:5:10:5$

The perimeter of trapezoid is $44$

Formula used:

Here, we are using the formula

Area of trapezoid = $\frac{1}{2}\left(a+b\right)h$

(here, “ a ” is upper base, “ b ” is lower base and “h” is height)

Calculation:

  

Here, let x be side of an isosceles trapezoid.

Perimeter of trapezoid = $44$

  $2x+5x+10x+5x=44$ (perimeter of trapezoid = sum of all sides)

  $22x=44$

  $x=2$

Now, sides of trapezoid are:

  $2x=2\times 2=4$

  $5x=5\times 2=10$

  $10x=10\times 2=20$

  $5x=5\times 2=10$

Now, In $\Delta ACE$

  ${\left(hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  ${\left(AC\right)}^2={\left(AE\right)}^2+{\left(CE\right)}^2$

  ${\left(10\right)}^2={\left(AE\right)}^2+{\left(8\right)}^2$

  ${\left(AE\right)}^2=100-64$

  ${\left(AE\right)}^2=36$

  $AE"h"=6$

Now, Area of trapezoid = $\frac{1}{2}\left(a+b\right)h$

(here, “ a ” is upper base, “ b ” is lower base and “h” is height)

→ $\frac{1}{2}\left(4+20\right)\times 6$

→ $72$

Conclusion: Hence,the area of the trapezoid is $72$ square units.