Chapter 8.4, Problem 62PFA

To determine

To determine polynomial represents the area of the colored triangles in square inches from the given options.

Answer to Problem 62PFA

  $2x^2+16x+32$ Or option (c)

Explanation of Solution

Given:

  

Base $=x+4$

Height $=x+4$

Formula used:

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

  ${(a+b)}^2=a^2+2ab+b^2$

Calculation:

From the given figure,

  

Base $=x+4$

Height $=x+4$

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

  $\Rightarrow$ Area of triangle $=\frac{1}{2}\times (x+4)\times (x+4)$

  $\Rightarrow$ Area of triangle $=\frac{1}{2}\times {(x+4)}^2$

  $\Rightarrow$ Area of triangle $=\frac{1}{2}\times (x^2+8x+16)$ [ $\because$ ${(a+b)}^2=a^2+2ab+b^2$ ]

  $\Rightarrow$ Area of triangle $=\frac{x^2}{2}+4x+8$

Now this represents the area of one triangle,

Area of the total four triangles is,

  $\Rightarrow$ Area of four triangles $=4\times (\frac{x^2}{2}+4x+8)$

  $\Rightarrow$ Area of four triangles $=2x^2+16x+32$

So, the area of total four triangles is $2x^2+16x+32$ or option (c).

Conclusion:

Therefore, the area of total four triangles is $2x^2+16x+32$ or option (c).