Math Problem Statement
Solution
Let's solve the problem step by step.
1. Area of the Triangle
The formula for the area of a triangle is given by:
In the triangle shown:
- Base = 6 units
- Height = 8 units
2. Area of the Rectangle
The formula for the area of a rectangle is:
In the rectangle shown:
- Length = 13 units
- Width = 8 units
3. Total Area
Now, to find the total area of the trapezoid (which is composed of the triangle and the rectangle), we add the areas of the triangle and the rectangle:
Final Answer:
- Area of the triangle: 24 square units
- Area of the rectangle: 104 square units
- Total area: 128 square units
Let me know if you'd like any further details or have any questions!
Related Questions:
- How do you calculate the area of a trapezoid directly without dividing it into shapes?
- How would the areas change if the triangle’s height were increased?
- What happens to the total area if both the base of the triangle and the length of the rectangle are doubled?
- How does the formula for the area of a triangle relate to that of a rectangle?
- What other ways can you decompose a trapezoid into simpler shapes?
Tip:
Always make sure to label the base and height of the triangle correctly—these must be perpendicular to each other for the area formula to work!
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Math Problem Analysis
Mathematical Concepts
Geometry
Area Calculation
Formulas
A_triangle = 1/2 * base * height
A_rectangle = length * width
Theorems
Area of a Triangle Theorem
Area of a Rectangle Theorem
Suitable Grade Level
Grades 6-8
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