Math Problem Statement

What is the formula A = 1/2 h(a + b) and how does it relate to finding the area?

Solution

The equation in the image is:

A=12h(a+b)A = \frac{1}{2} h(a + b)

This formula is commonly used to find the area AA of a trapezoid, where:

  • hh is the height of the trapezoid,
  • aa and bb are the lengths of the two parallel sides (the bases).

It works by averaging the lengths of the two bases aa and bb, multiplying by the height hh, and then multiplying the result by 12\frac{1}{2}.

Would you like more details or have any questions about this equation?

Here are five related questions:

  1. How do you derive this formula for the area of a trapezoid?
  2. How would this formula change if the trapezoid had equal bases?
  3. Can this formula be applied to any quadrilateral? Why or why not?
  4. How do you calculate the height of a trapezoid if it’s not given?
  5. What are some real-life applications where this formula might be useful?

Tip: Always make sure to verify that the shape is indeed a trapezoid (having two parallel sides) before applying this formula!

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Math Problem Analysis

Mathematical Concepts

Geometry
Trapezoid Area Calculation

Formulas

A = 1/2 h(a + b)

Theorems

Area of a Trapezoid Theorem

Suitable Grade Level

Grades 6-8