Question

look at this parallelogram. if both dimensions are halved, then which of the following statements about its area will be true? the ratio of the new area to the old area will be 4:1. the ratio of the new area to the old area will be 16:1. the ratio of the new area to the old area will be 1:2. the ratio of the new area to the old area will be 1:4.

Explanation:

Step1: Recall area formula of parallelogram

The area formula of a parallelogram is $A = base\times height$, denoted as $A_1=b_1h_1$.

Step2: Find new - area after halving dimensions

If the base and height are halved, the new base is $b_2=\frac{1}{2}b_1$ and the new height is $h_2=\frac{1}{2}h_1$. Then the new area $A_2 = b_2h_2=\frac{1}{2}b_1\times\frac{1}{2}h_1=\frac{1}{4}b_1h_1$.

Step3: Calculate the ratio of new area to old area

The ratio of the new area $A_2$ to the old area $A_1$ is $\frac{A_2}{A_1}=\frac{\frac{1}{4}b_1h_1}{b_1h_1}=\frac{1}{4}=1:4$.

Answer:

The ratio of the new area to the old area will be 1:4.