Chapter ISG, Problem 8.8STP

To determine

To write a polynomial that represent the area of figure.

Answer to Problem 8.8STP

Area of figure is $10x^2+9x-31$ .

Explanation of Solution

Given information:

A figure

Formula used:

Area of triangle= $\frac{1}{2}\times base\times height$

Area of rectangle= $length\times breadth$

Calculation:

For triangle,

  $base$ = $2x$

  $height$ = $3x-1$

For smaller rectangle,

  $length$ = $x+7$

  $breadth$ = $x-4$

For big rectangle,

  $length$ = $3x-1$

  $breadth$ = $2x+3$

Area of figure= (Area of triangle)+(area of rectangle)+(Area of rectangle)

Substituting value,

Area= $\frac{1}{2}\times 2x\times (3x-1)$ +{ $(3x-1)\times (2x+3)$ }+ $(x+7)\times (x-4)$

Solving equation,

Area= $(3x^2-2x)+(6x^2+9x-2x-3)+(x^2-4x+7x-28)$

Adding like terms,

Area= $(3x^2+6x^2+x^2-2x+9x-2x-4x+7x-28-3)$

So,

Area= $10x^2+9x-31$

Hence, area of figure is $10x^2+9x-31$ .