Using the Properties of Trapezoids to Solve Problems
Learning Outcomes
- Use properties of trapezoids
The formula for the area of a trapezoid is:
[latex-display]{\text{Area}}_{\text{trapezoid}}=\Large\frac{1}{2}\normalsize h\left(b+B\right)[/latex-display]
Splitting the trapezoid into two triangles may help us understand the formula. The area of the trapezoid is the sum of the areas of the two triangles. See the image below.
Splitting a trapezoid into two triangles may help you understand the formula for its area.
The height of the trapezoid is also the height of each of the two triangles. See the image below.
The formula for the area of a trapezoid is
If we distribute, we get,
Properties of Trapezoids
- A trapezoid has four sides.
- Two of its sides are parallel and two sides are not.
- The area, [latex]A[/latex], of a trapezoid is [latex]\text{A}=\Large\frac{1}{2}\normalsize h\left(b+B\right)[/latex] .
example
Find the area of a trapezoid whose height is [latex]6[/latex] inches and whose bases are [latex]14[/latex] and [latex]11[/latex] inches. SolutionStep 1. Read the problem. Draw the figure and label it with the given information. | |
Step 2. Identify what you are looking for. | the area of the trapezoid |
Step 3. Name. Choose a variable to represent it. | Let [latex]A=\text{the area}[/latex] |
Step 4.Translate. Write the appropriate formula. Substitute. | |
Step 5. Solve the equation. | [latex]A={\Large\frac{1}{2}}\normalsize\cdot 6(25)[/latex] [latex-display]A=3(25)[/latex-display] [latex]A=75[/latex] square inches |
Step 6. Check: Is this answer reasonable? | [latex]\checkmark[/latex] see reasoning below |
try it
[ohm_question]146533[/ohm_question]example
Find the area of a trapezoid whose height is [latex]5[/latex] feet and whose bases are [latex]10.3[/latex] and [latex]13.7[/latex] feet.Answer: Solution
Step 1. Read the problem. Draw the figure and label it with the given information. | |
Step 2. Identify what you are looking for. | the area of the trapezoid |
Step 3. Name. Choose a variable to represent it. | Let A = the area |
Step 4.Translate. Write the appropriate formula. Substitute. | |
Step 5. Solve the equation. | [latex]A={\Large\frac{1}{2}}\normalsize\cdot 5(24)[/latex] [latex-display]A=12(5)[/latex-display] [latex]A=60[/latex] square feet |
Step 6. Check: Is this answer reasonable? The area of the trapezoid should be less than the area of a rectangle with base [latex]13.7[/latex] and height [latex]5[/latex], but more than the area of a rectangle with base [latex]10.3[/latex] and height [latex]5[/latex]. | [latex]\checkmark[/latex] |
Step 7. Answer the question. | The area of the trapezoid is [latex]60[/latex] square feet. |
try it
[ohm_question]146534[/ohm_question]example
Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of [latex]3.4[/latex] yards and the bases are [latex]8.2[/latex] and [latex]5.6[/latex] yards. How many square yards will be available to plant?Answer: Solution
Step 1. Read the problem. Draw the figure and label it with the given information. | |
Step 2. Identify what you are looking for. | the area of a trapezoid |
Step 3. Name. Choose a variable to represent it. | Let [latex]A[/latex] = the area |
Step 4.Translate. Write the appropriate formula. Substitute. | |
Step 5. Solve the equation. | [latex]A={\Large\frac{1}{2}}\normalsize(3.4)(13.8)[/latex] [latex]A=23.46[/latex] square yards. |
Step 6. Check: Is this answer reasonable? Yes. The area of the trapezoid is less than the area of a rectangle with a base of [latex]8.2[/latex] yd and height [latex]3.4[/latex] yd, but more than the area of a rectangle with base [latex]5.6[/latex] yd and height [latex]3.4[/latex] yd. | |
Step 7. Answer the question. | Vinny has [latex]23.46[/latex] square yards in which he can plant. |
try it
[ohm_question]146535[/ohm_question]Contribute!
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- Question ID 146533, 146534, 146535. Authored by: Lumen Learning. License: CC BY: Attribution.
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- Ex: Find the Area of a Trapezoid. Authored by: James Sousa (mathispower4u.com). License: CC BY: Attribution.
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