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 77 units.
  • The height of the outer rectangle is 44 units.

So, the area of the outer rectangle is: Areaouter=7×4=28square units\text{Area}_{\text{outer}} = 7 \times 4 = 28 \, \text{square units}

Step 3: Calculate the area of the cut-out rectangle

  • The width of the cut-out is 22 units.
  • The height of the cut-out is 22 units.

So, the area of the cut-out rectangle is: Areacut-out=2×2=4square units\text{Area}_{\text{cut-out}} = 2 \times 2 = 4 \, \text{square units}

Step 4: Subtract the area of the cut-out from the outer rectangle

Total Area=AreaouterAreacut-out=284=24square units\text{Total Area} = \text{Area}_{\text{outer}} - \text{Area}_{\text{cut-out}} = 28 - 4 = 24 \, \text{square units}

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:

  1. How would the area change if the dimensions of the cut-out increased?
  2. What is the perimeter of this shape?
  3. How do you find the area of irregular shapes in general?
  4. How can you apply the same method to find the volume of a 3D shape with a cut-out?
  5. 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