Trapezoid

Scott Solomon

Trapezoid = Flat Four-Sided Shape with Two Parallel Sides

trapezoid


Basics
h = height
\bf\displaystyle{{b}_{1}} = length of side \bf\displaystyle{{b}_{1}}
\bf\displaystyle{{b}_{2}} = length of side \bf\displaystyle{{b}_{2}}
A = Area = area covering surface of trapezoid

Side \bf\displaystyle{{b}_{1}} and Side \bf\displaystyle{{b}_{2}} are parallel.


Formulas (Mathematics Formula Sheet)
\bf\displaystyle A=\frac{1}{2}h({{b}_{1}}+{{b}_{2}})
Parentheses protect order of operations.


Formulas (NOT on Mathematics Formula Sheet)
\bf\displaystyle h=\frac{2A}{({{b}_{1}}+{{b}_{2}})}
Parentheses protect order of operations.


Question
A trapezoidal window is 1200 centimeters tall and its parallel sides are 500 and 800 centimeters long, respectively.  What is its area?

Answer
780000 square centimeters

Answer Process
\bf\displaystyle A=\frac{1}{2}h({{b}_{1}}+{{b}_{2}})

\bf\displaystyle A=\frac{1}{2}\times1200({{500}}+{{800}}) = 780000

Input Display Comment
clear blinker clears screen
fraction 1 down 2 right × 1200
( 500 + 800 )		 \bf\displaystyle \frac{1}{2}*1200({{500}}+{{800}}) \bf\displaystyle A=\frac{1}{2}h({{b}_{1}}+{{b}_{2}})
enter 780000 Answer
Trapezoid


Question
With reference to the question above, what is the area of the window in square meters?

Answer
78 square meters

Answer Process
See Measurement.
Square Meters = Square Centimeters ÷ 10000 square centimeters per square meter
Square Meters = 780000 ÷ 10000 = 78 square meters

Input Display Comment
clear blinker clears screen
fraction 1 down 2 × 1200
( 500 + 800 )		 \bf\displaystyle \frac{1}{2}*1200({{500}}+{{800}}) \bf\displaystyle A=\frac{1}{2}h({{b}_{1}}+{{b}_{2}})
enter 780000
780000 ÷ 10000 780000÷10000 Square Meters = Square Centimeters ÷ 10000 square centimeters per square meter
enter 78 Answer
Trapezoid


Question
A trapezoidal window is \bf\displaystyle12\frac{1}{2} meters tall and its parallel sides are \bf\displaystyle5\frac{1}{2} and \bf\displaystyle8\frac{1}{4} meters long, respectively.  To the nearest tenth of a square meter, what is its area?

Answer
85.9 square meters

Answer Process
\bf\displaystyle A=\frac{1}{2}h({{b}_{1}}+{{b}_{2}})

\bf\displaystyle A=\frac{1}{2}\times12\frac{1}{2}(5\frac{1}{2}+8\frac{1}{4}) = \bf\displaystyle\frac{1375}{16} = 85.9375 = 85.9 after rounding

Input Display Comment
clear blinker clears screen
fraction 1 down 2 right ×
2nd mixed number 12 right 1 down 2 right
( 2nd mixed number 5 right 1 down 2 right
+ 2nd mixed number 8 right 1 down 4 )		 \bf\displaystyle \frac{1}{2}*12\frac{1}{2}(5\frac{1}{2}+8\frac{1}{4}) \bf\displaystyle A=\frac{1}{2}h({{b}_{1}}+{{b}_{2}})
enter \bf\displaystyle\frac{1375}{16}
toggle 85.9375 Answer
(before rounding)
Trapezoid


Question
A trapezoidal window has parallel sides that are 600 and 700 centimeters long, respectively.  Its area is 650000 square centimeters.  What is its height?

Answer
1000 centimeters

Answer Process
\bf\displaystyle h=\frac{2A}{({{b}_{1}}+{{b}_{2}})}

\bf\displaystyle h=\frac{2\times650000}{(600+700)} = 1000

Input Display Comment
clear blinker clears screen
fraction 2 × 650000 down
( 500 + 800 ) right		 \bf\displaystyle \frac{2*650000}{(600+700)} \bf\displaystyle h=\frac{2A}{({{b}_{1}}+{{b}_{2}})}
enter 1000 Answer
Trapezoid


Practice – Questions
1.  A trapezoidal solar panel is 1500 centimeters tall and its parallel sides are 500 and 700 centimeters long, respectively.  What is its area?

2.  A trapezoidal solar panel is 1400 centimeters tall and its parallel sides are 600 and 900 centimeters long, respectively.  What is its area?

3.  With reference to Question 2, what is the area of the panel in square meters?

4.  A trapezoidal solar panel is \bf\displaystyle14\frac{1}{2} meters tall and its parallel sides are \bf\displaystyle6\frac{1}{2} and \bf\displaystyle9\frac{1}{4} meters long, respectively.  To the nearest tenth of a square meter, what is its area?

5.  A trapezoidal solar panel has parallel sides that are 600 and 900 centimeters long, respectively.  Its area is 900000 square centimeters.  What is its height?


Practice – Answers
1.  900000 square centimeters

2.  1050000 square centimeters

3.  105 square meters

4.  114.2 square meters

5.  1200 centimeters

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