Chapter 11.1, Problem 47PPE

To determine

Write a ratio in simplified form of the area of the shaded figure to the area of the figure enclosed it.

Answer to Problem 47PPE

  ${\text{A}}_{\text{shaded}}:{\text{A}}_{\text{Trapezoid}}=1:(5x+6)$

Explanation of Solution

Given:

The figure:

Write a ratio in simplified form of the area of the shaded figure to the area of the figure enclosed it.

Concept Used:

The shaded region is a square. Area of square: $\text{A=}\text{Side}·\text{Side}$

The shape of the figure in which the shared region is enclosed is a Trapezoid.

Area of Trapezoid: ${\text{A}}_{\text{Trapezoid}}\text{=}\frac{1}{2}·(\text{sum}\text{of}\text{parallel}\text{sides})·\text{height}$

Calculation:

The shaded region is a square. Area of square: $\text{A=}\text{Side}·\text{Side}$

The shape of the figure in which the shared region is enclosed is a Trapezoid.

Area of Trapezoid: ${\text{A}}_{\text{Trapezoid}}\text{=}\frac{1}{2}·(\text{sum}\text{of}\text{parallel}\text{sides})·\text{height}$

Area of Square or shaded region: ${\text{A}}_{\text{shaded}}\text{=}\text{5}x·\text{5}x=25x^2$

Area of Trapezoid: ${\text{A}}_{\text{Trapezoid}}\text{=}\frac{1}{2}·(5x+5x+12)·5x=(5x+6)·5x$

Ratio: $\frac{{\text{A}}_{\text{shaded}}}{{\text{A}}_{\text{Trapezoid}}}=\frac{\text{5}x·\text{5}x}{(5x+6)·5x}=\frac{1}{5x+6}$

Thus, ${\text{A}}_{\text{shaded}}:{\text{A}}_{\text{Trapezoid}}=1:(5x+6)$