# WRITING EQUATIONS USE THE AREA OF A TRAPEZOID

## About "Writing equations using the area of a trapezoid"

Writing equations using the area of a trapezoid :

Here we are going to see how to use equations to solve problems based on the shape trapezium.

Steps involved :

• First we have to draw the picture by using the given details
• Write the formula to find the area of trapezoid.
• Substitute the given values.
• By using the inverse operations, we can find the the unknown.

## Writing equations using the area of a trapezoid - Examples

Example 1 :

A garden in the shape of a trapezoid has an area of 44.4 square meters. One base is 4.3 meters long and the other base is 10.5 meters long. The height of the trapezoid is the width of the garden. How wide is the garden?

Solution :

Given :

Area of trapezoid  =  44.4 square meters --- (1)

base length  =  10.5 m and 4 m

Formula to find area of trapezoid  =

(1/2) x h  (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h  (a + b)  =  44.4

(1/2) x h  (10.5 + 4)  =  44.4

(1/2) x h  x 14.5   =  44.4

Multiplying 2 on both sides, we get

h x 14.5  =  44.4 x 2

Dividing 14.5 on both sides, we get

h  =  (44.4 x 2)/14.5

h  = 6.12 approximately 6 m

Example 2 :

The cross section of a water trough is shaped like a trapezoid. The bases of the trapezoid are 18 feet and 8 feet long. It has an area of 52 square feet.What is the height of the cross section?

Solution :

Given :

Area of trapezoid  =  52 square feet --- (1)

base length  =  18 ft and 8 ft

Formula to find area of trapezoid  =

(1/2) x h  (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h  (a + b)  =  52

(1/2) x h  (18 + 8)  =  52

(1/2) x h  x 26   =  52

Multiplying 2 on both sides, we get

h x 26  =  52 x 2

Dividing 26 on both sides, we get

h  =  104/26

h  = 4 feet

Example 3 :

The top of a desk is shaped like a trapezoid. The bases of the trapezoid are 26.5 and 30 centimeters long. The area of the desk is 791 square centimeters. The height of the trapezoid is the width of the desk. Write and solve an equation to find the width of the desk.

Solution :

Given :

Area of trapezoid  =  791 square centimeters --- (1)

base length  =  26.5 and 30 centimeters

Formula to find area of trapezoid  =

(1/2) x h  (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h  (a + b)  =  791

(1/2) x h  (26.5 + 30)  =  791

(1/2) x h  x 56.5   =  791

Multiplying 2 on both sides, we get

h x 56.5  =  791 x 2

Dividing 56.5 on both sides, we get

h  =  791/56.5

h  = 14 centimeter

Example 4 :

A section in a stained glass window is shaped like a trapezoid. The top base is 4 centimeters and the bottom base is 2.5 centimeters long. If the area of the section of glass is 3.9 square centimeters, how tall is the section?

Solution :

Given :

Area of trapezoid  =  39 square centimeters --- (1)

base length  =  4 and 2.5 centimeters

Formula to find area of trapezoid  =

(1/2) x h  (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h  (a + b)  =  39

(1/2) x h  (4 + 2.5)  =  39

(1/2) x h  x 6.5   =  39

Multiplying 2 on both sides, we get

h x 6.5  =  39 x 2

Dividing 6.5 on both sides, we get

h  =  78/6.5

h  = 12 centimeter

Example 5 :

The cross section of a metal ingot is a trapezoid. The cross section has an area of 39 square centimeters.The top base of the cross section is 12 centimeters. The length of the bottom base is 2 centimeters greater than the top base. How tall is the metal ingot? Explain

Solution :

Given :

Area of trapezoid  =  39 square centimeters --- (1)

Length of top base = 12 centimeters

Length of bottom base = 12 + 2 = 14 centimeter

Formula to find area of trapezoid  =

(1/2) x h  (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h  (12 + 14)  =  39

(1/2) x h  (26)  =  39

Multiplying 2 on both sides, we get

h x 26  =  39 x 2

Dividing 6.5 on both sides, we get

h  =  78/26

h  = 3 centimeters

## Related topics

After having gone through the stuff given above, we hope that the students would have understood "Writing equations using the area of a trapezoid".

Apart from the stuff given above, if you want to know more about "Writing equations using the area of a trapezoid", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6