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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Trapezoids

Find the value of if the area of the trapezoid below 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 .

$60=\frac{1}{2}(12+c)6$

120=(12+c)6

12+c=20

c=8

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Example Question #42 : Trapezoids

Find the value of if the area of the trapezoid below is 210 .

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 .

$210=\frac{1}{2}(18+d)14$

420=(18+d)14

18+d=30

d=12

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Example Question #303 : Intermediate Geometry

The area of the trapezoid below is . Find the length of .

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 .

8^2+(CE)^2=10^2

64+(CE)^2=100

(CE)^2=36

CE=6

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 .

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

$96=\frac{1}{2}(12+AE+8)(6)$

$\frac{1}{2}(AE+20)=16$

AE+20=32

AE=12

The question asks you to find the length of .

AD=AE+ED

AD=12+8=20

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Example Question #41 : Trapezoids

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

Possible Answers:

Cannot be determined from the information given.

11.56

12.15

9.42

Correct answer:

12.15

Explanation:

First, draw in the height .

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

$\sin 47=\frac{CE}{8}$

$CE=8 \sin 47=5.85$

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

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

$56=\frac{1}{2}(7+AD)(5.85)$

$\frac{1}{2}(7+AD)=9.57$

7+AD=19.15

AD=12.15

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Example Question #43 : Trapezoids

The area of the trapezoid below is 244 . Find the length of . Round to the nearest hundredths place.

Possible Answers:

56.23

67.41

94.12

57.12

Correct answer:

57.12

Explanation:

First, draw in the height.

10a

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

$\sin 62=\frac{height}{8}$

$height=8\sin 62=7.06$

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

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

$244=\frac{1}{2}(12+AD)(7.06)$

$\frac{1}{2}(12+AD)=34.56$

12+AD=69.12

AD=57.12

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Example Question #304 : Intermediate Geometry

The area of the trapezoid below is 124 . Find the length of . Round to the nearest hundredths place.

Possible Answers:

19.54

16.34

15.25

11.14

Correct answer:

15.25

Explanation:

First, draw in the height.

11a

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

$\sin 58=\frac{height}{10}$

$height=10\sin 58=8.48$

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

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

$124=\frac{1}{2}(14+AD)(8.48)$

$\frac{1}{2}(14+AD)=14.62$

14+AD=29.25

AD=15.25

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Example Question #44 : Trapezoids

Given: Quadrilateral ABCD such that $\overline{AB} \parallel \overline{CD}$ and $\overline{AD} \ncong \overline{BC}$

True, false, or undetermined: Quadrilateral ABCD is a trapezoid.

Possible Answers:

True

False

Undetermined

Correct answer:

True

Explanation:

Quadrilateral ABCD has at least one pair of parallel sides, $\overline{AB}$ and $\overline{CD}$ . The figure is, by definition, a parallelogram if and only if $\overline{AD} \parallel \overline{BC}$ , and, by definition, a trapezoid if and only if $\overline{AD} \nparallel \overline{BC}$ . Opposite sides of a parallelogram are also congruent; since $\overline{AD} \ncong \overline{BC}$ , Quadrilateral ABCD is not a parallelogram. It is therefore a trapezoid.

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Example Question #45 : Trapezoids

A trapezoid has height 20 inches and area 640 square inches. Which of these choices can represent the lenghts of the two bases of the trapezoid?

Possible Answers:

32 inches and 32 inches

2 inches and 60 inches

18 inches and 44 inches

25 inches and 35 inches

27 inches and 37 inches

Correct answer:

27 inches and 37 inches

Explanation:

We can apply the area formula here.

$A = \frac{1}{2} h \left ( B+b\right )$

$640 = \frac{1}{2}\cdot 20 \left ( B+b\right )$

$640 = 10 \left ( B+b\right )$

B + b = 64

The sum of the bases must be 64 inches. We check each one of these choices, except for 32 inches and 32 inches, which can be eliminated as the bases cannot be of the same length.

27+37=64

25+35=60

18+44=62

2+60=62

Only 27 and 37 have 64 as a sum, so this is the correct choice.

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Example Question #1 : How To Find If Kites Are Similar

A kite has two different side lengths of and . Find the measurements for a similar kite.

Possible Answers:

and

Correct answer:

and

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides. In order for two kites to be similar their sides must have the same ratios.

Since, the given kite has side lengths and , they have the ratio of 4:12=1:3 .

Therefore, find the side lengths that have a ratio of 1:3 .

The only answer choice with this ratio is: 8:24=1:3

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Example Question #305 : Plane Geometry

A kite has two different side lengths of and . Find the measurements for a similar kite.

Possible Answers:

and

Correct answer:

and

Explanation:

A kite is a geometric shape that has two sets of equivalent adjacent sides. In order for two kites to be similar their sides must have the same ratios.

The given side lengths for the kite are and , which have the ratio of 1:4 .

The only answer choice with the same relationship between side lengths is: and , which has the ratio of 1:4.

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All Intermediate Geometry Resources

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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #41 : Trapezoids

Example Question #42 : Trapezoids

Example Question #303 : Intermediate Geometry

Example Question #41 : Trapezoids

Example Question #43 : Trapezoids

Example Question #304 : Intermediate Geometry

Example Question #44 : Trapezoids

Example Question #45 : Trapezoids

Example Question #1 : How To Find If Kites Are Similar

Example Question #305 : Plane Geometry

All Intermediate Geometry Resources

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