Bellwork
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Bellwork 10-2 Find the values of x and y for each 1. 2. 3. 30° x y 5 45° x 4 y 30° x 10 y
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Bellwork. Find the values of x and y for each 1. 2. 3. 10. 4. y. y. y. 5. 30°. 45°. 30°. x. x. x. 10-2. 10.2 Area of Regular Polygons. Radius:. The distance from the center to a vertex. Apothem:. - PowerPoint PPT Presentation
Transcript of Bellwork
Bellwork
10-2
Find the values of x and y for each1. 2. 3.
30°x
y5
45°x
4y
30°x
10y
Radius:The distance from the center to a vertex Apothem: The perpendicular distance from the center to a side
10.2 Area of Regular Polygons
10-2
m 1 = = 60 Divide 360 by the number of sides.360 6
m 3 = 180 – (90 + 30) = 60 The sum of the measures of the angles of a triangle is 180.
m 1 = 60, m 2 = 30, and m 3 = 60.
A regular hexagon has an apothem and radii drawn. Find the
measure of each numbered angle.
m 2 = m 1 The apothem bisects the vertex angle of the isosceles triangle formed by the radii.
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m 2 = (60) = 30 Substitute 60 for m 1.12
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3
Area of Regular Polygons
10-2
A regular octagon has an apothem and radii drawn. Find the
measure of each numbered angle.
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3
Area of Regular Polygons
10-2
A square has an apothem and radii drawn. Find the measure
of each numbered angle.
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Area of Regular Polygons
10-2
Area of a regular Polygon
The area of a regular polygon is half the product of the apothem and the perimeter
Area = ½ap
Area of Regular Polygons
10-2
Find the area of a regular polygon with twenty 12-in. sides
and a 37.9-in. apothem.
Find the perimeter p = ns
p = (20)(12) = 240 Substitute 20 for n and 12 for s.
A = 4548 Simplify.
The area of the polygon is 4548 in.2
A = (37.9)(240) Substitute 240 for p.12
A = ap Area of a regular polygon12
Area of Regular Polygons
A = (37.9)(p) Substitute 37.9 for a.12
10-2
8
Find the area of an equilateral triangle with apothem
8 cm. Leave your answer in simplest radical form.
Area of Regular Polygons
10-2
Find the area of an regular hexagon with radius 10m.
Leave your answer in simplest radical form.
Area of Regular Polygons
10-2
Consecutive radii form an isosceles triangle, so an apothem bisects the side of the octagon.
A library is in the shape of a regular octagon. Each side is 18.0
ft. The radius of the octagon is 23.5 ft. Find the area of the
library to the nearest 10 ft2.
To apply the area formula A = ap, you need to find a and p.
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Area of Regular Polygons
10-2
Step 2: Find the perimeter p.
p = ns Find the perimeter.
p = (8)(18.0) = 144 Substitute 8 for n and 18.0 for s,
and simplify.
(continued)
Step 1: Find the apothem a.
a2 + (9.0)2 = (23.5)2 Pythagorean Theorem
a2 + 81 = 552.25 Solve for a.
a2 = 471.25
a 21.7
Area of Regular Polygons
10-2
To the nearest 10 ft2, the area is 1560 ft2.
(continued)
Step 3: Find the area A.
A = ap Area of a regular polygon
A (21.7)(144) Substitute 21.7 for a and 144 for p.
A 1562.4 Simplify.
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Area of Regular Polygons
10-2
Composite Figures
10-3
A composite figure is a figure comprised of simple shapes (rectangle, circle, parallelogram, etc.)
Composite Figures
10-3
To find the area of a composite figure divide the figure into non-overlapping shapes of polygons that we have formulas for their areas.
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104
3 8
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Composite Figures
10-3
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3 38
Composite Figures
10-3
A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red. To dye 6 in2 of fabric, 2 oz of dye is needed. How much dye is needed for the entire order?
Composite Figures
10-3
HOMEWORK
10.2(691): 14,26,29
10.3(697):15,17,19,20
Area of Regular Polygons
