Question

1. rhombus a has a base of 7 inches and a height of 5 inches. rhombus b has a base and height that are three times the base and height of rhombus a. find the area of rhombus b and compare it to the area of rhombus a. explain.

Explanation:

Step1: Calculate Area of Rhombus A

The area of a rhombus is given by $\text{Area} = \text{base} \times \text{height}$.
For Rhombus A: $\text{Area}_A = 7 \times 5 = 35$ square inches

Step2: Find dimensions of Rhombus B

Base of B: $3 \times 7 = 21$ inches
Height of B: $3 \times 5 = 15$ inches

Step3: Calculate Area of Rhombus B

$\text{Area}_B = 21 \times 15 = 315$ square inches

Step4: Compare the two areas

Find the ratio: $\frac{\text{Area}_B}{\text{Area}_A} = \frac{315}{35} = 9$

Answer:

The area of Rhombus A is 35 square inches, and the area of Rhombus B is 315 square inches. The area of Rhombus B is 9 times the area of Rhombus A. This is because when both the base and height of a two-dimensional shape are scaled by a factor of $k$, the area scales by a factor of $k^2$ (here $k=3$, so $3^2=9$).