Respuesta :
The question is incomplete. So, here is the complete question.
The figure shown (in the attachment) is a rectangle. The green shape in the figure is a square. The blue and white shapes are rectangles and the area of the blue rectangle is 24 square inches. A.) Write an expression for the area of the entire figure that includes one exponent. Then find the area. B.) Find the dimensions of the entire figure.
Answer: A.) The expression is [tex]A_{t} = (2*6) + (8*3) + (6^{2} )[/tex] and total area is 72 square inches.
B.) width = 8in and length = 9in.
Step-by-step explanation: Area of a rectangle is A = width*length.
From the figure, we know the area and the measurements of the white rectangle: width = 2 inches; length = 6 inches.
So the area for white is [tex]A_{w}[/tex] = 2*6
The green shape is a square, which means width = length. So, [tex]A_{g}[/tex] = 6*6
For the blue shape:
length = length of green + width of white
length = 6+2 = 8
To determine the width, we use the area of blue.
[tex]A_{b}[/tex] = length*width
width = [tex]\frac{A_{b} }{length}[/tex]
width = [tex]\frac{24}{8}[/tex]
width = 3
So, the area of the entire figure is [tex]A_{t} = A_{w} + A_{b} + A_{g}[/tex]
Substituing, we have:
A.) [tex]A_{t} = A_{w} + A_{b} + A_{g}[/tex]
[tex]A_{t} = (2*6) + (8*3) + (6^{2} )[/tex]
[tex]A_{t}[/tex] = 72 square inches
B.) The dimensions of the entire figure are:
width = 6 + 2 = 8 in
length = 6 + 3 = 9 in
Therefore, the figure has 8 inches of width and 9 inches of length.
