Math Problem Statement

Find the area of the trapezoid

Find the area of the trapezoid.

Solution

The area of a trapezoid can be calculated using the formula:

Area=12×(b1+b2)×h\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h

Where:

  • b1b_1 and b2b_2 are the lengths of the two parallel sides (the bases),
  • hh is the height (the perpendicular distance between the two parallel sides).

From the image you provided:

  • The top base (b1b_1) is 10 ft,
  • The bottom base (b2b_2) is 12 ft,
  • The height (hh) is 6 ft.

Now, let's substitute these values into the formula:

Area=12×(10+12)×6\text{Area} = \frac{1}{2} \times (10 + 12) \times 6 Area=12×22×6\text{Area} = \frac{1}{2} \times 22 \times 6 Area=11×6=66 square feet\text{Area} = 11 \times 6 = 66 \text{ square feet}

So, the area of the trapezoid is 66 square feet.

Let me know if you'd like further clarification or if you have any more questions!


  1. How do I calculate the area of other shapes, such as parallelograms or triangles?
  2. What other formulas involve the same approach of adding two measurements and multiplying by a height or length?
  3. Can I apply this method to irregular quadrilaterals?
  4. How do I calculate the perimeter of a trapezoid?
  5. What happens to the area of the trapezoid if the height changes?

Tip: Always ensure the height is perpendicular to the parallel sides for the area formula to work correctly.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Trapezoid
Trapezoid Properties

Formulas

Area = 1/2 * (b1 + b2) * h

Theorems

Trapezoid Area Theorem

Suitable Grade Level

Grades 7-9