Chapter 8.5, Problem 45PPS

a.

To determine

To determine the expression in factorised form to represent the area of blue section.

Answer to Problem 45PPS

  $a\times b=ab$

Explanation of Solution

Given:

  

Length of Blue section = $b$

Breadth of Blue section = $a$

Formula used / Concept used:

Area of rectangle = $x\times y$

Calculation / Explanation:

  $\Rightarrow$ Length of Blue section = $b$

  $\Rightarrow$ Breadth of Blue section = $a$

  $\Rightarrow$ Area of rectangle blue section= $a\times b$

= $ab$

Conclusion: So, the area of the blue section is ab.

b.

To determine

To determine the expression in factorised form to represent the area formed by the outer edge.

Answer to Problem 45PPS

  $ab+6a+6b+36$

Explanation of Solution

Given:

  

Length of outer section = $b+3+3$

Breadth of outer section = $a+3+3$

Formula used / Concept used:

Area of rectangle = $x\times y$

Calculation / Explanation:

  $\Rightarrow$ Length of Blue section = $b+3+3$ (by adding both the extra sides of $3$ units)

  $\Rightarrow$ Breadth of Blue section = $a+3+3$ (by adding both the extra sides of $3$ units)

Here $x$ = $a+3+3$ and $y$ = $a+3+3$ ,

So, area formed by the outer edge,

  $\Rightarrow$ Area of rectangle = $(a+3+3)\times (b+3+3)$

= $(a+6)\times (b+6)$

= $(a+6)\times (b+6)$

= $a\times b+6\times b+6\times a+36$

= $ab+6b+6a+36$

Conclusion: So, the area formed by the outer edge is $ab+6b+6a+36$ .

c.

To determine

To determine the expression in factorised form to represent the area formed by the yellow region.

Answer to Problem 45PPS

  $6a+6b+36$

Explanation of Solution

Given:

  

Length of Blue section = $b$

Breadth of Blue section = $a$

Length of outer section = $b+3+3$

Breadth of outer section = $a+3+3$

Formula used / Concept used:

Area of rectangle = $x\times y$

Subtraction of polynomial.

Calculation / Explanation:

From the above two, the area of rectangle blue section= $ab$ and the area outer edge is $ab+6b+6a+36$ .

The area formed by the yellow region will be = area of outer edge $-$ area of rectangle blue section,

  $\Rightarrow$ area formed by the yellow region = $ab+6b+6a+36-ab$

  $\Rightarrow$ area formed by the yellow region = $6b+6a+36$

Conclusion: So, the area formed by the yellow region is $6b+6a+36$ .