# 9.4 Use properties of rectangles, triangles, and trapezoids  (Page 8/17)

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The height of a trapezoid is $7$ centimeters and the bases are $4.6$ and $7.4$ centimeters. What is the area?

42 sq. cm

The height of a trapezoid is $9$ meters and the bases are $6.2$ and $7.8$ meters. What is the area?

63 sq. m

Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of $3.4$ yards and the bases are $8.2$ and $5.6$ yards. How many square yards will be available to plant?

## 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 A = the area Step 4. Translate. Write the appropriate formula. Substitute. Step 5. Solve the equation. 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 8.2 yd and height 3.4 yd, but more than the area of a rectangle with base 5.6 yd and height 3.4 yd. Step 7. Answer the question. Vinny has 23.46 square yards in which he can plant.

Lin wants to sod his lawn, which is shaped like a trapezoid. The bases are $10.8$ yards and $6.7$ yards, and the height is $4.6$ yards. How many square yards of sod does he need?

40.25 sq. yd

Kira wants cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are $18$ feet and $14$ feet and whose height is $15$ feet, how many square feet of pavers will he need?

240 sq. ft

## Key concepts

• Properties of Rectangles
• Rectangles have four sides and four right (90°) angles.
• The lengths of opposite sides are equal.
• The perimeter, $P$ , of a rectangle is the sum of twice the length and twice the width.
• $P=2L+2W$
• The area, $A$ , of a rectangle is the length times the width.
• $A=L\cdot W$
• Triangle Properties
• For any triangle $\Delta ABC$ , the sum of the measures of the angles is 180°.
• $m\angle A+m\angle B+m\angle C=180°$
• The perimeter of a triangle is the sum of the lengths of the sides.
• $P=a+b+c$
• The area of a triangle is one-half the base, b, times the height, h.
• $A=\frac{1}{2}bh$

## Practice makes perfect

Understand Linear, Square, and Cubic Measure

In the following exercises, determine whether you would measure each item using linear, square, or cubic units.

amount of water in a fish tank

cubic

length of dental floss

living area of an apartment

square

floor space of a bathroom tile

height of a doorway

linear

capacity of a truck trailer

In the following exercises, find the perimeter and area of each figure. Assume each side of the square is $1$ cm.

1. 10 cm
2. 4 sq. cm

1. 8 cm
2. 3 sq. cm

1. 10 cm
2. 5 sq. cm

Use the Properties of Rectangles

In the following exercises, find the perimeter and area of each rectangle.

The length of a rectangle is $85$ feet and the width is $45$ feet.

1. 260 ft
2. 3825 sq. ft

The length of a rectangle is $26$ inches and the width is $58$ inches.

A rectangular room is $15$ feet wide by $14$ feet long.

1. 58 ft
2. 210 sq. ft

how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
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Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
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Kristine 2*2*2=8
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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J, combine like terms 7x-4y
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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