Math Problem Statement
Solution
From the image, the problem is asking to find the value of so that the areas of a trapezoid and a rectangle are the same.
The formula for the area of a trapezoid is given as:
where:
- is the height (6 ft in the trapezoid),
- and are the lengths of the two parallel sides (one is 12 ft, and the other is ).
The formula for the area of a rectangle is:
where:
- The length is 12 ft,
- The width is 6 ft.
Step-by-step solution:
-
Area of the trapezoid:
-
Area of the rectangle:
-
Equating the areas:
-
Solving for :
So, the value of is 12 feet.
Would you like more details or have any questions about this? Here are some related questions:
- How can you check the areas of both shapes after finding ?
- What would happen if was smaller or larger than 12 ft?
- Can you apply this method to any trapezoid and rectangle?
- How do you solve for if both shapes have different dimensions?
- Why does the equation involve adding the base lengths of the trapezoid?
Tip: Always ensure to substitute the correct values into area formulas to avoid errors in calculations.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Area Calculations
Formulas
Area of trapezoid: A = (1/2)h(b1 + b2)
Area of rectangle: A = length × width
Theorems
Equal Area Theorem
Suitable Grade Level
Grades 7-9
Related Recommendation
Solve for x by equating the area of a rectangle and a triangle
Solve for x in a Trapezoid with Algebraic Side Lengths
Solve for x in an Isosceles Trapezoid Using Trigonometry
Solving for x: Equating the Area of a Rectangle and Triangle
Solving for Height Using the Trapezoid Area Formula with Given Base Lengths