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Chapter 10: Area - PowerPoint PPT Presentation

Chapter 10: Area. Geometry Mrs. Cutbirth. Directions.

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Chapter 10: Area

Geometry

Mrs. Cutbirth

The button will take you to the first slide. If you are having trouble with a particular problem you may click the button to view a hint. The button will return you to the previously view slide. The slide will advance you to the next slide. The button will take you back a slide. When you complete the problem you may check your answer by clicking the answer button on the slide.

a ≈ __________

s= 107.5 cm

A = 19,887.5 cm2

Answer

P ≈ ___________

a = 38.6 mm

A = 4940.8 mm2

Answer

Answer

Regular n-gon: a = 9.6 cm and A = 302.4 cm2, P ≈ _______

Answer

Find the perimeter of a regular polygon if

a = 9m and A ≈ 259.2 m2

S

D

N

R

O A

5.

Answer

Find the shaded area of AORNGIS of the regular octagon ROADSIGN. The apothem measures about 20 cm. Segment GI measures about 16.6 cm.

Answer

An interior designer created the kitchen plan shown. The countertop will be constructed of colored concrete. What is its total surface area? If concrete countertops 1.5 inches thick cost \$85 per square foot, what will be the total cost of this countertop?

Answer

Find the sum of the interior angles in the polygon. Then find the value of p.

Sum of interior angles = _______

p = _______

Answer

The measure of an exterior angle of a regular octagon is x + 7. Find xand the measure of each exterior angle of the octagon.

Answer

Suppose a regular polygon has n sides. Write an expression to describe each of the following quantities for that regular polygon.

the sum of the measures of the interior angles

the measure of each interior angle

the sum of the measures of the exterior angles (one at each vertex)

the measure of each exterior angle.

Answer

Find the area of the trapezoid. A = ___________

28 cm

22 cm

Answer

Find the area. A=___________

Answer

In the figure at the right, quadrilateral WXYZ is a trapezoid.

Explain why ∆WXY and ∆XYZ have the same area (Hint: Consider XY as the base of both triangles.)

Use the answer in part a and the Area Addition Postulate to explain why ∆WXR and ∆RYZ have the same area.

THE END!

Your test is tomorrow. It will cover all of the material from chapter 10.

Exit

a ≈ __________

s= 107.5 cm

A = 19,887.5 cm2

Plug in for A and s, then solve your equation.

P ≈ ___________

a = 38.6 mm

A = 4940.8 mm2

Plug in for A and a, then solve your equation.

Regular n-gon: a = 9.6 cm and A = 302.4 cm2, P ≈ _______

Plug in for A and a, then solve your equation.

Find the perimeter of a regular polygon if

a = 9m and A ≈ 259.2 m2

Plug in for A and a, then solve your equation.

S

D

N

R

O A

5. Hint

Find the shaded area of AORNGIS of the regular octagon ROADSIGN. The apothem measures about 20 cm. Segment GI measures about 16.6 cm.

Find the area of the regular polygon using the formula, .

a = apothem

s = side length (GI)

n = number of sides

Then multiply that value by the fraction of the polygon that is shaded. What fraction of the total sides is shaded?

1. The shape is made up of two rectangles and one regular octagon.

3. To calculate the cost you will need to know how many square feet you have. If your area is in in2, you will need to do a conversion. There are 144in2 in 1ft2.

2. The apothem is the

distance from the

center to the side.

24 in

Find the sum of the interior angles in the polygon. Then find the value of p.

• Sum of interior angles = _______

• p = _______

Where n = the number of sides

To find p, set up and equation.

Add up all of the angles and set them equal to the sum you found.

The measure of an exterior angle of a regular octagon is x + 7. Find xand the measure of each exterior angle of the octagon.

The sum of the exterior angles is 360o. To find one exterior angle, divide the sum by the number of sides. To calculate x you can then set up an equation.

Find the area of the trapezoid. A = ___________

+

h= perpendicular height

and are the parallel bases

Find the area. A=___________

A =

The b and h must be perpendicular.

28 cm

22 cm

a =

P = 256mm

P = 63cm

P = 57.6 m

A = 996 cm2

A = 50 ft2 or 7200 in2

Cost = \$4250

Sum = 900

p = 50

x = 38

45o

• (n – 2)180

• 360

A = 297 in2

A = 308 cm2

• The area formula for a triangle is A = ½ bh. Both triangles share the same base and have the same height.

• Both triangles have the same area. If you subtract the same area from each triangle, then the remaining amount on each triangle will be the same.