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 x,10,8x
We cannot see the figures on these posts.
I don't know how to post the figure
We can't do it on these posts.
To find two algebraic expressions for the area of the figure, we will consider it as one large rectangle and then as a sum of four smaller rectangles. Let's break it down step by step.
1. Considering the figure as one large rectangle:
Let's call the length of the rectangle L and the width W.
- The area of the large rectangle is given by the formula: A_l = L * W.
- In our case, the length of the rectangle can be represented as (x + 10) (since it consists of a segment of length x and an additional segment of length 10).
- The width of the rectangle is 8x.
- Therefore, the algebraic expression for the area of the figure, considering it as one large rectangle, is: A_l = (x + 10) * 8x.
2. Considering the figure as a sum of four smaller rectangles:
In this case, the figure can be divided into two vertical segments and two horizontal segments.
- The area of the figure can be calculated as the sum of the areas of these four smaller rectangles.
- Let's consider the two vertical segments as rectangle A and rectangle B, and the two horizontal segments as rectangle C and rectangle D.
- The length of rectangle A is x, and the width is 10.
- The length of rectangle B is x, and the width is 10.
- The length of rectangle C is 8x, and the width is 10.
- The length of rectangle D is 8x, and the width is 10.
- Therefore, the algebraic expression for the area of the figure, considering it as a sum of four smaller rectangles, is: A_s = (x * 10) + (x * 10) + (8x * 10) + (8x * 10).
So, the two algebraic expressions for the area of the figure would be:
1. A_l = (x + 10) * 8x (considering the figure as one large rectangle)
2. A_s = (x * 10) + (x * 10) + (8x * 10) + (8x * 10) (considering the figure as a sum of four smaller rectangles)