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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q23. (page 432)

Use a calculator or the trigonometry table on page 311to find the area of each figure to the nearest tenth.

Short Answer

Expert verified

The area of given figure is approximately $73.5$ square unit.

Step by step solution

01

Step 1. Modify the given figure.

Draw the perpendicular $A E = h$

02

Step 2. Concept Used.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Use trigonometric Ratios

$\begin{array}{l} \sin θ = \frac{Opposite}{H y p o t e n u s e} \\ \sin 50^{\circ} = \frac{h}{8} \\ h = 6.128 \end{array}$

03

Step 3. Find the area of parallelogram.

Area of parallelogram can be found using the formula

$\begin{matrix} A = b h \\ = (12) (6.128) \\ = 73.54 \\ \approx 73.5 \end{matrix}$

Therefore, the area of given figure is $73.5$ Square unit.

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Most popular questions from this chapter

The area of a rectangle is $55 c m^{2}$ and height 5cm.What is the base?

a. Use the diagram at the right. Find the area of $▱ P Q R S$ .

b. Use the diagram at the right. Find the area of $△ P S R$ .

c. Use the diagram at the right. Find the area of $△ O S R$ . (Hint: Refer to $△ P S R$ and use Exercise28).

d. Use the diagram at the right. What is the area of $△ P S O$ ?

e. Use the diagram at the right. What must the area of $△ P O Q$ be? Why? What must the area of $△ O Q R$ be?

f. Use the diagram at the right. State what you have shown in parts (a)-(e) about how the diagonals of a parallelogram divide the parallelogram.

Is the actual area of the shaded region more or less than the value given by computer program? Explain

The base of a rectangle is $(x + 5)$ and height $(x)$ . What is the area and perimeter of the rectangle?

Find the area of each figure:

A square inscribed in a circle with radiusr.

See all solutions

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