Question

The irregular figure on the left has been decomposed into the figures on the right.

A figure is broken into a parallelogram and rectangle. The rectangle has a base of 7 centimeters and a height of 4 centimeters. The parallelogram has a base of 7 centimeters and a height of 5 centimeters.
What is the value of w, the width of the parallelogram?
4 centimeters
5 centimeters
7 centimeters
9 centimeters

Answer 1

To find the width \( w \) of the parallelogram, we'll first look at the given dimensions of both the rectangle and the parallelogram.

1. **Rectangle:**
- Base = 7 cm
- Height = 4 cm

The area of the rectangle is given by the formula:
\[
\text{Area}_{\text{rectangle}} = \text{base} \times \text{height} = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2
\]

2. **Parallelogram:**
- Base = 7 cm
- Height = 5 cm
- We need to find the width \( w \), which is the length of the sides parallel to the height.

The area of the parallelogram is given by the formula:
\[
\text{Area}_{\text{parallelogram}} = \text{base} \times \text{height} = 7 \, \text{cm} \times 5 \, \text{cm} = 35 \, \text{cm}^2
\]

The problem doesn't directly state that \( w \) is related to any calculations of areas. Since the base is given as 7 cm and height as 5 cm for the parallelogram, the width \( w \) typically refers to the base of the parallelogram.

Thus, the value of \( w \) is:

\[
\text{\( w = 7 \, \text{cm} \)}
\]

So, the correct answer is \( 7 \, \text{centimeters} \).