The perimeter of the figure below is 154cm. assume all angles are right angles.
a) what is the value of x?
b) what is the area of the figure

Okay. So to start this problem, you will have to write an equation that adds all of the sides and sets it equal to the total perimeter that is already given. 

(6x + 5) + (6x + 5) + (2x) + (2x) + (2x) + (2x) + (2x) + (2x) = 154

Now add everything together. 

When you add everything together you should get :
24x + 10 = 154

Now solve to find x. 

Start by subtracting 10 from both sides. 

24x + 10 = 154
24x = 144

Now divide both sides by 24 to get x alone. 

24x = 144
x = 6

There is the first part of your answer. 

Now to find the area of this shape. You will have to do it in parts.

First, multiply the length times the width for the rectangle. Be careful to include the full measurement. 

2x * (6x + 5 + 2x) 
2x * (8x + 5)
16x^2 + 10x
This is the area of part of the shape.

Now find the area of the square.

2x * 2x = 4x^2
This is the area of the area of the second part of the shape.

Now add the two areas together. 

4x^2 + 16x^2 + 10
20x^2 + 10

So your answers are : 

1) x = 6   and 
2) 20x^2 + 10 cm^2