Question

what is the perimeter of this block? 28.2 + 28.2 + 4x + 6.4 + 4x + 6.4 = what is the area of this block? 28.2 · 4x + 6.4 =

Explanation:

Step1: Simplify the perimeter expression

Combine like terms:

$$\begin{align*} &28.2 + 28.2+(4x + 6.4)+(4x + 6.4)\\ =&(28.2\times2)+(4x+4x)+(6.4\times2)\\ =&56.4 + 8x+12.8\\ =&8x+(56.4 + 12.8)\\ =&8x + 69.2 \end{align*}$$

Step2: Simplify the area expression

Use the distributive property \(a(b + c)=ab+ac\) (where \(a = 28.2\), \(b = 4x\), \(c = 6.4\)):

$$\begin{align*} &28.2\times(4x + 6.4)\\ =&28.2\times4x+28.2\times6.4\\ =&112.8x+180.48 \end{align*}$$

Answer:

Perimeter: \(8x + 69.2\) yd; Area: \(112.8x+180.48\) yd²