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
To find two algebraic expressions for the area of the figure, let's first analyze the figure. The figure can be regarded as one large rectangle and as a sum of four smaller rectangles.
1. Regarding the figure as one large rectangle:
Let the length of the large rectangle be L and the width be W.
Therefore, the area of the figure can be expressed as A₁ = L × W.
2. Regarding the figure as a sum of four smaller rectangles:
Let the lengths of the smaller rectangles be t, t, 5, and 3, and their widths be 5, W, 3, and W.
The first smaller rectangle has a length of t and width of 5, so its area is A₂₁ = 5t.
The second smaller rectangle has a length of t and width of W, so its area is A₂₂ = tW.
The third smaller rectangle has a length of 5 and width of 3, so its area is A₂₃ = 15.
The fourth smaller rectangle has a length of 3 and width of W, so its area is A₂₄ = 3W.
Adding up the areas of the four smaller rectangles, the total area of the figure can be expressed as A₂ = A₂₁ + A₂₂ + A₂₃ + A₂₄. Simplifying this expression yields A₂ = 5t + tW + 15 + 3W.
So, we have the following two algebraic expressions for the area of the figure:
1. Regarding the figure as one large rectangle: A₁ = L × W.
2. Regarding the figure as a sum of four smaller rectangles: A₂ = 5t + tW + 15 + 3W.