Find the area of this shape.
Understand the Problem
The question is asking to find the area of a given geometric shape with specified dimensions. To solve it, we will break down the shape into simpler rectangles and calculate their areas, then sum those areas to find the total.
Answer
$10 \, \text{m}^2$
Answer for screen readers
The area of the shape is $10 , \text{m}^2$.
Steps to Solve
- Identify the shape components
The shape can be divided into two rectangles:
- Rectangle 1 (the large rectangle)
- Rectangle 2 (the smaller indent)
- Calculate the area of Rectangle 1
Rectangle 1 has dimensions:
- Width = 3 m
- Height = 4 m
The area is calculated as: $$ A_1 = \text{width} \times \text{height} = 3 , \text{m} \times 4 , \text{m} = 12 , \text{m}^2 $$
- Calculate the area of Rectangle 2
Rectangle 2 has dimensions:
- Width = 1 m
- Height = 2 m
The area is calculated as: $$ A_2 = \text{width} \times \text{height} = 1 , \text{m} \times 2 , \text{m} = 2 , \text{m}^2 $$
- Find the total area
To obtain the area of the original shape, we subtract the area of Rectangle 2 from Rectangle 1: $$ A_{\text{total}} = A_1 - A_2 = 12 , \text{m}^2 - 2 , \text{m}^2 = 10 , \text{m}^2 $$
The area of the shape is $10 , \text{m}^2$.
More Information
The area calculation by breaking down irregular shapes into manageable rectangles is a common technique in geometry. Understanding how to manipulate these dimensions can simplify more complex problems in real-world contexts, such as landscaping, architecture, and land surveying.
Tips
- Forgetting to subtract the area of the smaller rectangle from the larger one.
- Miscalculating the dimensions or area of each rectangle.
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