200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Basic Polygon Stuff Polygon Angles Basic Area Probability.

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Presentation transcript:

Basic Polygon Stuff Polygon Angles Basic Area Probability Area of Regular Polygons

What three things must be true in order for a figure to be a polygon?

Closed figure Line segments Sides only intersect at endpoints

What is the difference between a convex polygon and a concave polygon?

A concave polygon is “caved in”. All diagonals of a convex polygon lie inside the polygon.

What is a regular polygon?

A regular polygon is one with all angles congruent and all sides congruent.

Classify each polygon by sides.

octagon dodecagon pentagon hexagon triangle undecagon

Why can’t a concave polygon be regular? Is a rhombus regular? Explain.

A concave polygon can not be regular because the angles will not be congruent. The polygon will have at least one angle greater than 180°. A rhombus is not always regular because the angles do not have to be congruent.

How do you find the sum of the exterior angles in a convex polygon?

It’s always 360°.

How do you find the sum of the interior angles in a convex polygon?

(# of sides – 2) 180°

Find the sum of the measures of the interior angles of each polygon. 52-gon

720° 9000°

Find the value for n. 88° 135° n°n° 110° 120°

88° 135° n°n° 110° 120° n = 540 n = 87°

88° 45° n°n° 80° 70° Find the value for n. 47°

88° 45° n°n° 80° 70° 47° n = 360 n = 30

Find the area. 13 cm 5 cm

13 5 = 65 cm²

Find the area. 25 cm 18 cm 16 cm

25 cm 18 cm 16 cm = 400 cm²

Find the area. 17 in. 23 in. 18 in.

17 in. 23 in. 18 in = 360 in.²

Find the area of the rhombus. 19 km 16 km

Area = ½ Area = 152 km²

9 m 18 m 10 m 16 m Find the area.

9 m 18 m 10 m 7 m 8 m = 198 m²

What is probability?

Probability is the study of chance, or how likely something is to happen.

What does a probability of 1 mean? What does a probability of 0 mean?

A probability of 1 means that an event is certain to happen. A probability of 0 means that an event is impossible – it can’t happen.

How likely is it that a point chosen at random will lie in the shaded region?

certain impossible Probable / likely unlikely

What is the difference between experimental probability and theoretical probability?

Experimental probability is based on the results of an experiment. Theoretical probability uses formulas and theories to predict what will probably happen.

Find the probability that a point chosen at random will lie in the shaded region

½ ½ P = = 45%

What is the formula for finding the area of a regular polygon?

Area = ½ perimeter apothem This only works for a regular polygon.

What is an apothem?

An apothem is drawn from the center of a regular polygon to a side. It is perpendicular to the side and it bisects the side.

Find the area of the regular polygon. 8.7 m 10 m

Perimeter = 60 Area = ½ Area = 261 m²

Find the area of the regular polygon. 18 m 23.5 m

18 m 23.5 m Perimeter = 144 Apothem = 9² + a² = 23.5² Apothem = 21.7 Area = ½ Area = m²

Find the area of the regular polygon. 30

360 / 5 = 72 72° 36° a cos 36 = a / 30 a = 24.3 b 24.3² + b² = 30² b = P = 176 Area =