Math Problem Statement

Work out the area of this shape. Give your answer in cm².

Solution

To calculate the area of the given shape, we will divide it into two parts: a rectangle and a triangle. Then, we'll calculate the area of each and sum them.

Dimensions:

  1. Rectangle:

    • Width = 4 cm
    • Height = 10 cm

    Area of rectangle=width×height=4×10=40cm2\text{Area of rectangle} = \text{width} \times \text{height} = 4 \times 10 = 40 \, \text{cm}^2

  2. Triangle:

    • Base = 4 cm
    • Height = 4 cm

    Area of triangle=12×base×height=12×4×4=8cm2\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8 \, \text{cm}^2

Total Area:

Total Area=Area of rectangle+Area of triangle=40+8=48cm2\text{Total Area} = \text{Area of rectangle} + \text{Area of triangle} = 40 + 8 = 48 \, \text{cm}^2

Final Answer:

The area of the shape is 48 cm².

Would you like further clarification or details on this?
Here are some additional related questions to consider:

  1. What is the formula for calculating the area of other composite shapes?
  2. How can we calculate the perimeter of this shape?
  3. How do we approach shapes with irregular outlines?
  4. How can we use a grid to estimate the area of such shapes?
  5. What are the key differences between 2D area and 3D volume calculations?

Tip: Always break down complex shapes into simpler components for easier calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Composite Shapes
Basic Shape Areas

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8