Question

aubrey claims that if the dimensions of the parallelogram shown are doubled, then the area of the larger parallelogram will be 4 times more than the original. which statement about her claim is completely true?

diagram of parallelogram with base 6 in, side 5 in, height 3 in

• aubrey is correct because the area of the new parallelogram is 12(6) = 72 square inches. the original area is 18 square inches. since 4(18) = 72, the new parallelogram has 4 times the area of the original.
• aubrey is correct because the area of the new parallelogram is 10(7) = 70 square inches. the original area is 18 square inches. since 4(18) = 72, it is about 4 times larger than the original.
• aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. the original area is 18 square inches so the new parallelogram will have an area of 2(18) = 36, or two times more than the original.
• aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. truncated text

Explanation:

Step1: Calculate the original area

The formula for the area of a parallelogram is \(A = base\times height\). For the original parallelogram, \(base = 6\) in and \(height=3\) in. So, \(A_{original}=6\times3 = 18\) square inches.

Step2: Calculate the new - area after doubling the dimensions

If we double the base and the height, the new base \(b = 2\times6=12\) in and the new height \(h = 2\times3 = 6\) in. Then \(A_{new}=12\times6=72\) square inches.

Step3: Check the relationship between the new and original areas

We want to find out how many times \(A_{new}\) is of \(A_{original}\). Let \(n=\frac{A_{new}}{A_{original}}\). Substitute \(A_{new} = 72\) and \(A_{original}=18\) into the formula: \(n=\frac{72}{18}=4\).

Answer:

Aubrey is correct because the area of the new parallelogram is \(12\times6 = 72\) square inches. The original area is 18 square inches. Since \(4\times(18)=72\), the new parallelogram has 4 times the area of the original.