Math Problem Statement
find area
Find the area of the shape in the image.
Solution
The shape in the image resembles a rectangular figure with a cut-out. To find the total area, we can follow these steps:
Step 1: Split the shape into two parts
- Main rectangle: The overall dimensions of the outer rectangle.
- Subtracted rectangle: The smaller rectangular cut-out at the bottom center.
Step 2: Calculate the area of the outer rectangle
- The width of the outer rectangle is units.
- The height of the outer rectangle is units.
So, the area of the outer rectangle is:
Step 3: Calculate the area of the cut-out rectangle
- The width of the cut-out is units.
- The height of the cut-out is units.
So, the area of the cut-out rectangle is:
Step 4: Subtract the area of the cut-out from the outer rectangle
Thus, the area of the given shape is 24 square units.
Would you like more details or have any questions?
Here are 5 related questions:
- How would the area change if the dimensions of the cut-out increased?
- What is the perimeter of this shape?
- How do you find the area of irregular shapes in general?
- How can you apply the same method to find the volume of a 3D shape with a cut-out?
- What are other examples of shapes that can be solved by subtraction like this?
Tip: When dealing with composite shapes, break them down into simpler parts to make area calculations easier.
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Composite Shapes
Formulas
Area of a rectangle = width × height
Theorems
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Suitable Grade Level
Grades 6-8