The figure shown 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 40 square inches.
Enter an expression for the area of the entire figure that includes an exponent. Then find the area.
An expression for the area of the entire figure is
The area is
110
square inches.
Part 2 out of 2
Find the dimensions of the entire figure.
The dimensions of the entire figure are
To find the dimensions of the entire figure, we need to analyze the given information.
We know that the blue rectangle's area is 40 square inches. Let's assume its length is l and its width is w.
Since the green shape is a square, its area is the square of its side length. Let's assume its side length is s.
And since the entire figure is a rectangle, we can determine its dimensions based on the dimensions of the blue rectangle and the green square.
The dimensions of the entire figure can be expressed as:
Length = l + 2s
Width = w + s
Now, we need to find values for l, w, and s.
Since the area of the blue rectangle is given as 40 square inches, we have:
l * w = 40
We also know that the green shape is a square, which means its side length is the same as its length or width. And since the blue rectangle is inside the green square, we can express the area of the green square in terms of the blue rectangle's dimensions as:
s^2 = l * w
s^2 = 40
To find the values of l, w, and s, we need more information or equations.
To find the expression for the area of the entire figure, we need to consider the areas of all the individual shapes.
The green shape is a square, so its area can be represented as x^2, where x is the length of the sides of the square.
The blue shape is a rectangle with an area of 40 square inches. Let's represent the length of one side of the rectangle as a and the length of the other side as b. Therefore, the area of the blue rectangle can be represented as a * b = 40.
The white shape is also a rectangle, but its dimensions are not given. So, let's represent the length of one side of the white rectangle as c and the length of the other side as d. Therefore, the area of the white rectangle can be represented as c * d.
To find the area of the entire figure, we add up the areas of all the shapes:
Area of entire figure = area of green shape + area of blue rectangle + area of white rectangle
= x^2 + (a * b) + (c * d)
Now, to find the area of the entire figure, we need the specific dimensions of each shape. Since the dimensions are not provided, we cannot calculate the exact area of the entire figure.
However, if we assume that the white rectangle has the same dimensions as the blue rectangle (a = c and b = d), then we can calculate the area.
Let's assume a = c = 5 inches and b = d = 8 inches. Plugging these values into the expression for the area of the entire figure, we get:
Area of entire figure = x^2 + (5 * 8) + (5 * 8)
= x^2 + 40 + 40
= x^2 + 80
Since we do not have any information about the length of the sides of the green square (x), we cannot calculate the exact area of the entire figure.
Therefore, the expression for the area of the entire figure is x^2 + 80 square inches, and the area cannot be determined without specific values for the dimensions.