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Intermediate Geometry : Intermediate Geometry

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Trapezoid

Find the perimeter of the trapezoid below.

Possible Answers:

214

300

200

234

210

Correct answer:

200

Explanation:

We can then use the Pythagorean Theorem to find the right portion of the bottom base. We can then use this value to determine the left portion.

Using Pythagorean Theorem again, we can calculate the left leg to be 20. That means we now know all four sides. The perimeter is simply the sum.

$\small P=20+52+34+94=200$

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Example Question #1 : How To Find The Perimeter Of A Trapezoid

An isosceles trapezoid has two bases that are parallel to each other. The larger base is times greater than the smaller base. The smaller base has a length of 2.5 inches and the length of non-parallel sides of the trapezoid have a length of 4.5 inches.

What is the perimeter of the trapezoid?

Possible Answers:

21.5in

10.5in

23in

11.5in

23.5in

Correct answer:

21.5in

Explanation:

To find the perimeter of this trapezoid, first find the length of the larger base. Then, find the sum of all of the sides. It's important to note that since this is an isosceles trapezoid, both of the non-parallel sides will have the same length.

The solution is:

The smaller base is equal to 2.5 inches. Thus, the larger base is equal to:

$2.5\times4=10$

Perimeter=base1+base2+(2S) , where the length of one of the non-parallel sides of the isosceles trapezoid.

$P=2.5+10+(2\times 4.5)$

P=2.5+10+9=21.5

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Example Question #1 : How To Find The Perimeter Of A Trapezoid

Dr. Robinson's property is shaped like an isosceles trapezoid. Dr. Robinson gave a contractor the following measurements, so that the contractor can build a wall around the enire property.

Measurements of property:

base1: 15 yds

base2:7.5yds

non-parallel-sides: 8yds

Find the perimeter of Dr. Robinson's property.

Possible Answers:

30.5

42yds

28.5yds

38.5yds

28yds

Correct answer:

38.5yds

Explanation:

The measurements that Dr. Robinson gave to the contractor include the lengths of the two base sides and one of the non-parallel sides of the property. Since Dr. Robinson's property is shaped like an isosceles trapezoid, there must be two non-parallel sides of equal length.

The solution is:

P=15+7.5+2(8)=15+7.5+16=38.5

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Example Question #121 : Quadrilaterals

Find the area of the following trapezoid.

Geo_area2

Possible Answers:

$152 ft^{2}$

$128 ft^{2}$

$190 ft^{2}$

$96 ft^{2}$

$160 ft^{2}$

Correct answer:

$128 ft^{2}$

Explanation:

The correct answer is 128 sq ft.

There are two ways to find the total area. One way to find the total area, you must find the area of the triangle and rectangle separately. After some deduction (19ft -13ft) , you can find that the base of the triangle is 6 ft. Then using the Pythagorean Theorem, or 3-4-5 right triangles, you can find that the height of the triangle and rectangle is 8 ft. Geo_area2b

To find the area of the triangle, you would multiply 6 by 8 and then divide by 2 to get 24. To find the area of the rectangle, you would multiply 8 by 13 to get 104. Then you would add both areas to get 128 sq ft.

Geo_area2c

The other way to find the area is to use the formula for area of a trapezoid. After some deduction (19ft -13ft) , you can find that the base of the triangle is 6ft. Then using the Pythagorean Theorem or 3-4-5 right triangles, you can find that the height of the triangle and rectangle is 8 ft.

Then you use the formula:

${\frac{1}{2}}h (b_{1} +b_{2})$

to get

$\frac{1}{2}\cdot 8(13+19)=128sq ft$

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Example Question #31 : Trapezoids

Find the length of if the area of the trapezoid below is 320 .

Possible Answers:

Cannot be determined from the information given.

Correct answer:

Explanation:

Start by drawing in the height, , to form a right triangle.

Use the Pythagorean Theorem to find the length of .

24^2+(CE)^2=26^2

576+(CE)^2=676

(CE)^2=100

CE=10

Now that we have the height, plug in the given information into the formula to find the area of the trapezoid.

Keep in mind that AE+ED=AD .

$\text{Area}=\frac{1}{2}(base_1+base_2)(height)$

$320=\frac{1}{2}(14+AE+24)(10)$

$\frac{1}{2}(AE+38)=32$

AE+38=64

AE=26

The question asks you to find the length of .

AD=AE+ED

AD=26+24=50

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Example Question #33 : Trapezoids

Find the length of . The area of the trapezoid is . Round to the nearest hundredths place.

Possible Answers:

11.77

10.45

8.94

9.02

Correct answer:

9.02

Explanation:

First, draw in the height .

First, find by using $\text{sine}$ .

$\sin 53=\frac{CE}{10}$

$CE=10\sin 53=7.99$

Now, plug in the values for area, height, and one base to find the length of the second base, .

$\text{Area}=\frac{1}{2}(base_1+base_2)(height)$

$60=\frac{1}{2}(6+AD)(7.99)$

$\frac{1}{2}(6+AD)=7.51$

6+AD=15.02

AD=9.02

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Example Question #34 : Trapezoids

Find the length of . The area of the trapezoid is 106 . Round to the nearest hundreths place.

Possible Answers:

6.01

10.00

12.04

8.06

Correct answer:

8.06

Explanation:

First, draw in the height.

First, find the height by using $\text{sine}$ .

$\sin 78=\frac{height}{12}$

$height=12 \sin 78=11.74$

Now, plug in the values for area, height, and one base to find the length of the second base, .

$\text{Area}=\frac{1}{2}(base_1+base_2)(height)$

$106=\frac{1}{2}(10+AD)(11.74)$

$\frac{1}{2}(10+AD)=9.03$

10+AD=18.06

AD=8.06

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Example Question #32 : Trapezoids

Find the length of . The area of the trapezoid is 500 . Round to the nearest hundredths place.

Possible Answers:

47.85

49.00

46.29

53.00

Correct answer:

49.00

Explanation:

First, draw in the height.

First, find the height by using $\text{sine}$ .

$\sin 66=\frac{height}{15}$

$height=15\sin 66=13.70$

Now, plug in the values for area, height, and one base to find the length of the second base, .

$\text{Area}=\frac{1}{2}(base_1+base_2)(height)$

$500=\frac{1}{2}(24+AD)(13.70)$

$\frac{1}{2}(24+AD)=36.50$

24+AD=73.00

AD=49.00

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Example Question #36 : Trapezoids

Find the value of if the area of this trapezoid is .

Possible Answers:

Correct answer:

Explanation:

The formula to find the area of a trapezoid is

$\text{Area}=\frac{1}{2}(base_1+base_2)(height)$ .

Substitute in the values for the area, a base, and the height. Then solve for .

$90=\frac{1}{2}(14+a)6$

180=(14+a)6

14+a=30

a=16

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Example Question #33 : Trapezoids

Find the value of if the area of this trapezoid is 130 .

Possible Answers:

Correct answer:

Explanation:

The formula to find the area of a trapezoid is

$\text{Area}=\frac{1}{2}(base_1+base_2)(height)$ .

Substitute in the values for the area, a base, and the height. Then solve for .

$130=\frac{1}{2}(17+b)5$

260=(17+b)5

17+b=52

b=35

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Trapezoid

Example Question #1 : How To Find The Perimeter Of A Trapezoid

Example Question #1 : How To Find The Perimeter Of A Trapezoid

Example Question #121 : Quadrilaterals

Example Question #31 : Trapezoids

Example Question #33 : Trapezoids

Example Question #34 : Trapezoids

Example Question #32 : Trapezoids

Example Question #36 : Trapezoids

Example Question #33 : Trapezoids

All Intermediate Geometry Resources

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