Chapter 38: Chapter 38

Problem 1153

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In parallelogram \(\mathrm{ABCD}, \mathrm{AB}=8\) inches, \(\mathrm{AD}=6\) inches, and angle \(\mathrm{A}=30^{\circ}\). Find the number of square inches in the area of the parallelogram.

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The area of parallelogram ABCD is \(24\) square inches.

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TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Sketch the parallelogram

Draw the parallelogram ABCD with sides AB and AD given, and the angle A between the two sides. Label the sides AB as 8 inches and AD as 6 inches, and the angle A as 30°.

Step 2: Find the height of the parallelogram

We need to find the height of the parallelogram, which is the perpendicular distance between the opposite sides (say, AB and CD). To find this height, we can use trigonometry. Let's call the height h. Since we are given that angle A is 30°, we can relate the height, side AD, and angle A, using the sine function: \[h = \text{AD} \times \sin(\text{angle A})\]

Step 3: Plug in the given values

Now, substitute the given values for side AD (6 inches) and angle A (30°) into the equation: \[h = 6 \times \sin(30°)\]

Step 4: Calculate the height

Calculate the height h: \[h = 6 \times 0.5 = 3\] The height of the parallelogram is 3 inches.

Step 5: Find the area of the parallelogram

Now that we have the height. We can calculate the area of the parallelogram using the formula: \[\text{Area} = \text{base} \times \text{height}\] In this case, base is side AB, which is given as 8 inches.

Step 6: Plug in the values in the formula

Now, substitute the given value for the base (8 inches) and the height we found earlier (3 inches) into the formula: \[\text{Area} = 8 \times 3\]

Step 7: Calculate the area

Compute the area: \[\text{Area} = 24\] The area of parallelogram ABCD is 24 square inches.

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Chapter 38: Chapter 38

In parallelogram \(\mathrm{ABCD}, \mathrm{AB}=8\) inches, \(\mathrm{AD}=6\) inches, and angle \(\mathrm{A}=30^{\circ}\). Find the number of square inches in the area of the parallelogram.

Short Answer

Step by step solution

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Step 1: Sketch the parallelogram

Step 2: Find the height of the parallelogram

Step 3: Plug in the given values

Step 4: Calculate the height

Step 5: Find the area of the parallelogram

Step 6: Plug in the values in the formula

Step 7: Calculate the area

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Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 20

Chapter 21

Chapter 22

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

Chapter 29

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Chapter 34

Chapter 35

Chapter 36

Chapter 37

Chapter 39

Chapter 40

Chapter 41

Chapter 42

Chapter 43

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Chapter 47

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