Which statements are true about the area of the figure? Check all that apply.

Question

A figure can be broken into 2 rectangles. One rectangle has a base of 3 and one-half and a height of 2 and one-half. The other rectangle has a base of one-half and a height of one-half.
The area can be found by multiplying 3 by 2One-half and adding the product of One-half and One-half.
The area can be found by multiplying 3 by 3 and one-half and then subtracting the product of 3 and One-half.
The area can be found by multiplying 3 by 2One-half and adding the product of 3 and One-half.
The area can be found by multiplying 3 by 3 and one-half and then subtracting the product of 2One-half and One-half.
The area can be found by multiplying 2One-half by 3One-half and adding the product of One-half and One-half.
The area is 7Three-fourths square units.
The area is 9One-fourth square units.
The area is 9 square units.

Answer 1

To solve for the area of the figure composed of two rectangles, we first need to calculate the area of each rectangle using the provided dimensions.

Rectangle 1:

• Base: \(3\frac{1}{2} = \frac{7}{2}\)
• Height: \(2\frac{1}{2} = \frac{5}{2}\)

The area of Rectangle 1 is given by: \[ \text{Area} = \text{Base} \times \text{Height} = \frac{7}{2} \times \frac{5}{2} = \frac{35}{4} \quad \text{(or 8.75)} \]

Rectangle 2:

• Base: \(\frac{1}{2}\)
• Height: \(\frac{1}{2}\)

The area of Rectangle 2 is given by: \[ \text{Area} = \text{Base} \times \text{Height} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]

Total Area:

Now, we find the total area by adding the areas of the two rectangles: \[ \text{Total Area} = \frac{35}{4} + \frac{1}{4} = \frac{36}{4} = 9 \]

Summary of Statements:

1. The area can be found by multiplying \(3\) by \(2\frac{1}{2}\) and adding the product of \(\frac{1}{2}\) and \(\frac{1}{2}\).

   • This is true. \(3 \times 2\frac{1}{2} = 8.75\) (which is \(\frac{35}{4}\)) and \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\). The sum is \(9\).

2. The area can be found by multiplying \(3\) by \(3\frac{1}{2}\) and then subtracting the product of \(3\) and \(\frac{1}{2}\).

   • This is false. The base \(3\frac{1}{2}\) is incorrect for this rectangle.

3. The area can be found by multiplying \(3\) by \(2\frac{1}{2}\) and adding the product of \(3\) and \(\frac{1}{2}\).

   • This is false. The second rectangle has a base of \(\frac{1}{2}\) not \(3\).

4. The area can be found by multiplying \(3\) by \(3\frac{1}{2}\) and then subtracting the product of \(2\frac{1}{2}\) and \(\frac{1}{2}\).

   • This is false. Not applicable calculations.

5. The area can be found by multiplying \(2\frac{1}{2}\) by \(3\frac{1}{2}\) and adding the product of \(\frac{1}{2}\) and \(\frac{1}{2}\).

   • This is false. Confusing dimensions again.

6. The area is \(7\frac{3}{4}\) square units.

   • This is false. The area is \(9\) square units.

7. The area is \(9\frac{1}{4}\) square units.

   • This is false. The area is \(9\) square units.

8. The area is \(9\) square units.

   • This is true.

True Statements:

• The area can be found by multiplying \(3\) by \(2\frac{1}{2}\) and adding the product of \(\frac{1}{2}\) and \(\frac{1}{2}\). (True)
• The area is \(9\) square units. (True)

Therefore, the true statements about the area of the figure are the first statement and the last statement.