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**Chapter 11 Length and Area**

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**11.1 Areas of Triangles and Parallelograms**

Area of a square = s2 Area of a rectangle = bh Area of a parallelogram = bh Area of a triangle = bh

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**Important Information**

If two polygons are congruent, then they have the same area. The area of a region is the sum of the areas of its non-overlapping parts.

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**11.2 Areas of Trapezoids, Rhombuses, and Kites**

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**Formulas Area of a trapezoid = h(b1 + b2) 2**

Area of a rhombus = d1 d

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More Formulas Area of a kite = d1 d

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Examples Find the area of RSTU. Find the area of the polygon RSTWUV.

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Example One diagonal of a kite is 1/3 as long as the other. The area of the kite is 0.24m2. What are the lengths of the diagonals?

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**11.3 Perimeter and Area of Similar Figures**

If two polygons are similar with the lengths of corresponding sides in the ratio a:b, then the ratio of their areas is a2:b2.

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**Example ABCD is similar to RSTU. Find the ratio of the perimeters.**

Find the ratio of the areas.

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Example You are painting 2 wall in an office complex that are similar in shape- both rectangles. One wall has a side length of 10ft. The corresponding side of the other wall is 14ft. You need 7 quarts to paint the larger wall. How many quart do you need for the smaller wall?

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Example The Pentagon in Washington DC is a regular pentagon with side lengths of 900ft. The area is 1,400,000ft2. The perimeter of a scale model of the building is 30yds. What is the area of the scale model?

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**11.4 Circumference and Arc length**

Circumference – the distance around the circle

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**Arc length- a portion of the circumference of a circle**

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Find the length of AB

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**Find the indicated measures.**

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**11.5 Area of Circles and Sectors**

Area of a circle A = πr2 Sector of a circle- region bounded by 2 radii of the circle and the intercepted arc. Sector APB = m AB πr o

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Example Find the area of the sectors formed by <HJK.

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Example Find the area between the large outer circle and the two smaller circles.

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**11.6 Areas of Regular Polygons**

The center of a polygon and the radius of a polygon are the center and radius of its circumscribed circle. Apothem of a polygon- distance from center to any side of a polygon Central Angle of a regular polygon- the angle formed by 2 radii drawn to consecutive vertices of the polygon

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Vocabulary Apothem Radius Central Angle

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Formula Area of a regular polygon A =

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Examples For a regular octagon inscribed in circle C, find the following: m<RCY = m<RCZ = M<ZYC =

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Example What is the area of a regular hexagon with a side length of 8 inches?

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Example What is the area of a regular decagon inscribed in a circle with a radius of 8mm?

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**11.7 Using Geometric Probability**

Probability (of an event) - P(A)- a measure of the likelihood that an event will occur. Geometric probability is a ratio that involves a geometric measure like length or area.

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Example Find the probability that a point chosen at random on AE is on CD. A B C D E

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Example A dart game uses targets with concentric circles of radii 5,8, and 12 inches. What is the probability the dart will earn 20 points?

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