Math Problem Statement

A=1/2h(b+b); A=44, B=4, B=7

Solution

To solve for hh using the formula A=12h(b1+b2)A = \frac{1}{2}h(b_1 + b_2), where:

  • AA is the area of a trapezoid,
  • hh is the height,
  • b1b_1 and b2b_2 are the lengths of the parallel sides (bases).

We are given:

  • A=44A = 44,
  • b1=4b_1 = 4,
  • b2=7b_2 = 7.

Let's substitute these values into the formula:

44=12h(4+7)44 = \frac{1}{2}h(4 + 7)

Now solve for hh:

44=12h(11)44 = \frac{1}{2}h(11)

44=112h44 = \frac{11}{2}h

Multiply both sides by 2 to get rid of the fraction:

88=11h88 = 11h

Now divide by 11:

h=8811=8h = \frac{88}{11} = 8

Thus, the height hh is 8 units.


Would you like a more detailed explanation or have any other questions?

Here are 5 related questions you can explore:

  1. How do you calculate the area of a triangle using a similar formula?
  2. How does the trapezoid area formula change when the bases are equal?
  3. Can you find the perimeter of the trapezoid with given side lengths?
  4. How does the area formula for trapezoids differ from that of parallelograms?
  5. What are real-world applications of trapezoid area calculations?

Tip: Always check if the dimensions are in consistent units when solving geometric problems.

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Math Problem Analysis

Mathematical Concepts

Geometry
Trapezoid Area Formula
Algebra

Formulas

A = 1/2h(b1 + b2)

Theorems

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Suitable Grade Level

Grades 6-8