Math Problem Statement

Work out the area of the given shape by splitting it into a triangle and a rectangle.

Solution

To calculate the area of the given shape, we can split it into two parts as suggested: a rectangle and a triangle.

  1. Rectangle Dimensions:

    • Width = 2cm2 \, \text{cm}
    • Height = 30cm30 \, \text{cm}

    The area of the rectangle is calculated as: Area of rectangle=width×height=2cm×30cm=60cm2\text{Area of rectangle} = \text{width} \times \text{height} = 2 \, \text{cm} \times 30 \, \text{cm} = 60 \, \text{cm}^2

  2. Triangle Dimensions:

    • Base = 8cm8 \, \text{cm}
    • Height = 2cm2 \, \text{cm}

    The area of the triangle is calculated as: Area of triangle=12×base×height=12×8cm×2cm=8cm2\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^2

  3. Total Area: The total area is the sum of the areas of the rectangle and the triangle: Total Area=Area of rectangle+Area of triangle=60cm2+8cm2=68cm2\text{Total Area} = \text{Area of rectangle} + \text{Area of triangle} = 60 \, \text{cm}^2 + 8 \, \text{cm}^2 = 68 \, \text{cm}^2

Final Answer: The total area of the shape is 68 cm².

Would you like further clarification or assistance with similar problems? Here are five related questions you might find helpful:

  1. How do you calculate the area of more complex composite shapes?
  2. What are the formulas for finding areas of various 2D shapes?
  3. How would the area calculation change if the triangle were not right-angled?
  4. How can you verify the area calculation using other methods?
  5. Can this approach be applied to real-world problems, like finding the area of irregular plots of land?

Tip: Always ensure dimensions are consistent (e.g., in the same units) when calculating areas!

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of composite shapes
Basic arithmetic

Formulas

Area of a rectangle = width × height
Area of a triangle = 1/2 × base × height

Theorems

N/A

Suitable Grade Level

Grades 6-8