Math Problem Statement

Find the area of the trapezoid, given a = 7.7 in and b = 2.1 in.

Solution

The figure shown in the image is a trapezoid, and we are asked to find its area. The formula to find the area of a trapezoid is given by:

Area=12×(a+b)×h\text{Area} = \frac{1}{2} \times (a + b) \times h

Where:

  • aa is the length of the top parallel side,
  • bb is the length of the bottom parallel side,
  • hh is the height of the trapezoid.

From the diagram, it's clear that the height hh is equal to the value labeled as aa (the vertical height), which is 7.7 inches. The base lengths are labeled as aa and bb, where a=7.7a = 7.7 inches (top) and b=2.1b = 2.1 inches (bottom).

Now, applying the formula:

Area=12×(7.7+2.1)×7.7\text{Area} = \frac{1}{2} \times (7.7 + 2.1) \times 7.7 Area=12×9.8×7.7\text{Area} = \frac{1}{2} \times 9.8 \times 7.7 Area=12×75.46\text{Area} = \frac{1}{2} \times 75.46 Area=37.73square inches\text{Area} = 37.73 \, \text{square inches}

Thus, the area of the trapezoid is 37.73 square inches.

Would you like more details or have any questions?

Here are five related questions you might consider:

  1. What would the area be if the height was different but the side lengths were the same?
  2. How would you calculate the perimeter of this trapezoid?
  3. What if the trapezoid had one non-parallel side—how would that affect the formula?
  4. How do we calculate the area of a triangle using a similar method?
  5. Can this formula be applied to 3D shapes like trapezoidal prisms?

Tip: Always double-check the units when performing area calculations to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Trapezoids

Formulas

Area = 1/2 * (a + b) * h

Theorems

Area formula for trapezoids

Suitable Grade Level

Grades 6-8