find two algebraic expressions for the area of each figure. first ,regard the figure as one large rectangle, and then regard the figure as a sum of four smaller rectangles 3 t,t,5
To find two algebraic expressions for the area of a figure, let's start by understanding the given information.
The figure is described as having dimensions of 3t, t, and 5. We can interpret this as the length, width, and height, respectively.
Finding the area when regarding the figure as one large rectangle:
When we consider the figure as one complete rectangle, the area can be determined by multiplying its length and width.
Area = Length × Width
= 3t × t
= 3t²
Hence, the algebraic expression for the area, when the figure is regarded as one large rectangle, is 3t².
Next, let's find the area when regarding the figure as a sum of four smaller rectangles:
In this case, we can divide the figure into four smaller rectangles, and then add up their individual areas to find the total area.
To divide the figure, we can consider two smaller rectangles stacked on top of each other, with dimensions of 3t and 5, and two smaller rectangles placed side by side, with dimensions of t and 5.
Area of the top rectangle = Length × Width
= 3t × 5
= 15t
Area of the bottom rectangle = Length × Width
= 3t × 5
= 15t
Area of the left rectangle = Length × Width
= t × 5
= 5t
Area of the right rectangle = Length × Width
= t × 5
= 5t
Adding up the areas of these four smaller rectangles:
Total Area = Area of top rectangle + Area of bottom rectangle + Area of left rectangle + Area of right rectangle
= 15t + 15t + 5t + 5t
= 40t
Therefore, the algebraic expression for the area of the figure, when regarded as a sum of four smaller rectangles, is 40t.