Find two algebraic expressions for the area of each figure. First, regard the figure as one large rectangle, and then regard the figure the figure as a sum of four smaller rectangles t,5,t,3
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To find two algebraic expressions for the area of the figure, we will consider two different approaches.
Approach 1: Regard the figure as one large rectangle
In this approach, we will find the area of the figure by considering it as one large rectangle. To determine the dimensions of this rectangle, we need to add the lengths of the sides together.
Looking at the figure described as a sum of four smaller rectangles t, 5, t, and 3, we can determine that the length of the large rectangle is (t + t) = 2t, and the width is (5 + 3) = 8.
Using the formula for the area of a rectangle (Area = Length × Width), we can express the area of the figure as:
Area = 2t × 8 = 16t.
So, the first algebraic expression for the area of the figure, considering it as one large rectangle, is 16t.
Approach 2: Regard the figure as a sum of four smaller rectangles
In this approach, we will find the area of the figure by considering it as a sum of four smaller rectangles. We can determine the dimensions of each rectangle using the given lengths.
The figure consists of two smaller rectangles with dimensions t × 5 and t × 3. So, the areas of these two rectangles are:
Area1 = t × 5 = 5t,
Area2 = t × 3 = 3t.
To find the total area, we need to add the areas of these rectangles together. Since the figure is also composed of two identical rectangles, we can double the sum of the areas to account for both sides.
Total Area = 2(Area1 + Area2) = 2(5t + 3t) = 2(8t) = 16t.
Therefore, the second algebraic expression for the area of the figure, considering it as a sum of four smaller rectangles, is also 16t.