Question

7-34.Find the perimeter and area of each algebra tile shape below. Be sure tocombine like terms.

Answer 1

We have the following:

a.

we have that the perimeter of a figure is the sum of all the sides

`\begin{gathered} p=(3)/(4)x+2x+(3)/(4)x+2x \\ p=(11)/(2)x \end{gathered}`

For the area:

`\begin{gathered} A=A_1+A_2+A_3 \\ A=(3)/(4)x\cdot(4)/(3)x+(1)/(2)x\cdot(1)/(2)x+(1)/(4)x\cdot(1)/(4)x \\ A=x^2+(x^2)/(4)+(x^2)/(16) \\ A=(21)/(16)x^2 \end{gathered}`

b.

For perimeter

`\begin{gathered} p=x+(7)/(4)x+x+(7)/(4)x \\ p=(11)/(2)x \end{gathered}`

For area:

`\begin{gathered} A=A_1+A_2+A_3 \\ A=x\cdot(1)/(4)x+(5)/(4)x\cdot(1)/(4)x+x\cdot(1)/(4)x \\ A=(13)/(16)x^2 \end{gathered}`