Charmaine’s backyard has a patio and a garden. Find the area of the garden. (Sides meet at right angles.)
The correct answer and explanation is:
To accurately find the area of Charmaine’s garden, details such as a diagram or specific measurements of the garden and patio are necessary. Since these measurements are not provided in the question, let’s assume a typical setup based on common problems of this nature:
Suppose Charmaine’s entire backyard is a rectangle measuring 20 meters long and 15 meters wide, and the patio is a smaller rectangle inside the backyard measuring 8 meters long and 5 meters wide. The garden would then be the remaining part of the backyard not occupied by the patio.
Step-by-Step Solution:
- Calculate the area of the entire backyard: Areabackyard=length×width=20×15=300 square meters\text{Area}_{\text{backyard}} = \text{length} \times \text{width} = 20 \times 15 = 300 \, \text{square meters}
- Calculate the area of the patio: Areapatio=8×5=40 square meters\text{Area}_{\text{patio}} = 8 \times 5 = 40 \, \text{square meters}
- Find the area of the garden by subtracting the patio from the backyard: Areagarden=Areabackyard−Areapatio=300−40=260 square meters\text{Area}_{\text{garden}} = \text{Area}_{\text{backyard}} – \text{Area}_{\text{patio}} = 300 – 40 = 260 \, \text{square meters}
Explanation:
The problem is based on basic concepts of area calculation for rectangles. When shapes meet at right angles, and all sides are either vertical or horizontal, calculating the area becomes a matter of multiplying length and width.
In this case, the entire backyard is one large rectangle, and the patio is another smaller rectangle located within it. To determine how much space is left for the garden, subtract the area of the patio from the total area of the backyard.
This type of problem illustrates how subtraction of areas is used in geometry when one part of a larger region is taken up by a non-overlapping smaller region. Always ensure units remain consistent and double-check all measurements. If an actual diagram was provided, identifying the shapes and dimensions visually would help ensure accuracy.