Lesson 3 Menu
15
1. Find the area of the figure. Round to the nearest tenth if necessary. 2. Find the area of the figure. Round to the nearest tenth if necessary. 3. Find the area of the figure. Round to the nearest tenth if necessary.
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Find the area of the figure. Round to the nearest tenth if necessary. 2.Find the area of the figure. Round to the nearest tenth if necessary. 3.Find the area of the figure. Round to the nearest tenth if necessary. Lesson 3 Menu. Find areas of regular polygons. - PowerPoint PPT Presentation
Transcript of Lesson 3 Menu
1. Find the area of the figure.
Round to the nearest tenth
if necessary.
2. Find the area of the figure.
Round to the nearest tenth
if necessary.
3. Find the area of the figure.
Round to the nearest tenth
if necessary.
• apothem
• Find areas of regular polygons.
• Find areas of circles.
Area of a Regular Polygon
Find the area of a regular pentagon with a perimeter of 90 meters.
Area of a Regular Polygon
Apothem: The central angles of a regular pentagon areall congruent. Therefore, the measure of
each angle is or 72. is an apothem
of pentagon ABCDE. It bisects and is
a perpendicular bisector of . So,
or 36. Since the perimeter
is 90 meters, each side is 18 meters and
meters.
Area of a Regular Polygon
Write a trigonometric ratio to find the length of .
Use a calculator.
Divide each side by tan .
Multiply each side by GF.
Area of a Regular Polygon
≈ 557
Answer: The area of the pentagon is about 557 square meters.
Simplify.
Area: Area of a regular polygon
A. A
B. B
C. C
D. D
A. 890 in2
B. 1225 in2
C. 991 in2
D. 1982 in2
Find the area of a regular pentagon with a perimeter of 120 inches. To the nearest square inch.
An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square yards.
The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So the diameter of the cover is 8 + 72 + 8 or 88 inches. Divide by 2 to find that the radius is 44 inches.
The area of the cover is 6082.1 square inches. To convert to square yards, divide by 1296.
Answer: The area of the cover is 4.7 square yards to the nearest tenth.
Area of a circle
Substitution
Use a calculator.
1. A
2. B
3. C
4. D
A. 31.0 yd2
B. 33.8 yd2
C. 1215.1 yd2
D. 43743.5 yd2
A swimming pool company manufactures circular covers for above ground pools. If the cover is 10 inches longer than the pool on each side, find the area of the cover in square yards.
Area of an Inscribed Polygon
Find the area of the shaded region. Assume that the triangle is equilateral. Round to the nearest tenth.
The area of the shaded region is the difference between the area of the circle and the area of the triangle. First, find the area of the circle.
Area of a circle
Substitution
Use a calculator.
Area of an Inscribed Polygon
To find the area of the triangle, use properties of 30-60-90 triangles. First, find the length of the base. The hypotenuse of so RS is 3.5 and SZ . Since .
Δ
Area of an Inscribed Polygon
Answer: The area of the shaded region is 153.9 – 63.7 or 90.3 square centimeters to the nearest tenth.
Use a calculator.
Area of a triangle
Next, find the height of the triangle, XS. Since m 3.5
